Slang expression“Vpiska” has been used in communication for a long time. In this post we will examine in detail the meaning of the word, which has become very popular among young people.
What does it mean?
So, in slang - an invitation to have fun at noisy company at someone's apartment. By the way, jargon appeared back in Soviet times, when young people were looking for a free apartment for entertainment and recreation.
Founders unusual word became members of the hippie subculture. The guys often traveled around the country and, due to lack of finances, stayed overnight in the houses or apartments of their friends, acquaintances, and even strangers. Such overnight stays were usually called “inscriptions”.
To date registrations for teenagers- these are visits to parties at home or in an apartment, which involve a subsequent overnight stay. Such gatherings promise to be noisy and lengthy. Alcoholic drinks are drunk at the registers.
Very often, such events are held at someone’s acquaintance’s place when parents of teenagers go on vacation or on a business trip. The most important thing is to have an empty apartment, house or even a dacha.
In some cases, registration on youth slang may mean temporarily staying in someone's apartment for a few days.
Main purpose of the event
What is the purpose of such parties? It's simple. The youth movement is organized away from adults, who often bore teenagers with teachings, instructions and advice. The guys want to be away from their elders and have fun.
By the way, sometimes registration is considered only as an overnight stay. For example, a person does not have money for a hotel or rent, but needs somewhere to spend the night. Or someone simply missed the last bus or tram, and the owner of the apartment, so as not to kick the guest out at such a late time, leaves it overnight (such cases are called “unplanned registration”).
Types of parties
What do they do at the so-called “registrations”? It all depends on the type of event. Now we will tell you in more detail about each of them.
Legion
One of the safest and most harmless entries. People who know each other very well come to such an event. They gather not only to drink alcohol, but also to interesting communication. A small nuance: initially guys gather at the legions, and then they invite unfamiliar girls to visit. This is often done through social media.
Flat
Another completely harmless type of entry. The guys get together just to do what they love together. This could be listening to music or playing computer games.
Submarine
Youth slang abounds similar expression. What does it mean? Turns out, Submarine- This is an unusual entry in which young people lock themselves in an apartment or in a country house in order to have fun. Its goal is renunciation familiar world. While the “submarine” lasts, you cannot leave the premises, house or apartment, it is forbidden to use mobile phones and electrical appliances.
On the side
Such registration is considered unsafe, because people who don’t know each other come to it. Another problem with the event is that it can be canceled at the last minute.
Road party
A party on the way somewhere. Usually young people gather in a sleeping car compartment.
Hustle
The word translated from English means “crush.” These are registrations with such a huge number of people that there is simply no room left in the apartment. free space. By the way, not all teenagers like this state of affairs. But on the other hand, this is a great opportunity to meet someone who will invite you to your next party.
Vpiska-sausage
A party to which none of the invited girls came.
How to get registered?
It's easy to get registered. You can simply use the search in social network"In contact with". It’s easy to find a user there who gathers guys at his home for a party for one or several nights.
But it is worth remembering that when attending such events, you should be careful, because the consequences can be the most unpredictable!
Are there any rules?
To “fit in” with any crowd you should know that there is certain rules behavior at such events.
A prerequisite is politeness towards those present. It is considered indecent to ask where to sleep in an apartment. The owner can indicate the sleeping place himself, but usually guests sit directly on the floor.
It is forbidden to take things that belong to the owner of the house and especially to take them outside the home without asking. You can use the telephone and bathroom only with the consent of the owner.
It is advisable to bring food and alcoholic drinks with you to registration!
Even more interesting information You can learn about registrations from the video:
Now you know everything about these parties!
"Circle" We have seen that a circle can be circumscribed around any triangle. That is, for every triangle there is a circle such that all three vertices of the triangle “sit” on it. Like this:
Question: can the same be said about a quadrilateral? Is it true that there will always be a circle on which all four vertices of the quadrilateral will “sit”?
It turns out that this is NOT TRUE! A quadrilateral can NOT ALWAYS be inscribed in a circle. There is a very important condition:
In our picture:
| . |
Look, the angles and lie opposite each other, which means they are opposite. What then about the angles and? They seem to be opposites too? Is it possible to take angles and instead of angles and?
Of course you can! The main thing is that the quadrilateral has some two opposite angles, the sum of which will be. The remaining two angles will then also add up by themselves. Do not believe? Let's make sure. Look:
Let be. Do you remember what the sum of all four angles of any quadrilateral is? Certainly, . That is - always! . But, → .
Magic right there!
So remember this very firmly:
If a quadrilateral is inscribed in a circle, then the sum of any two of it opposite corners equal to
and vice versa:
If a quadrilateral has two opposite angles whose sum is equal, then the quadrilateral is cyclic.
We will not prove all this here (if you are interested, look into the next levels of theory). But let's see what this remarkable fact leads to: that in an inscribed quadrilateral the sum of the opposite angles is equal.
For example, the question comes to mind: is it possible to describe a circle around a parallelogram? Let's try the “poke method” first.
Somehow it doesn't work out.
Now let's apply the knowledge:
Let's assume that we somehow managed to fit a circle onto a parallelogram. Then there must certainly be: , that is.
Now let's remember the properties of a parallelogram:
Every parallelogram has equal opposite angles.
It turned out that
What about the angles and? Well, the same thing of course.
Inscribed → →
Parallelogram→ →
Amazing, right?
It turns out that if a parallelogram is inscribed in a circle, then all its angles are equal, that is, it is a rectangle!
And at the same time - the center of the circle coincides with the intersection point of the diagonals of this rectangle. This is included as a bonus, so to speak.
Well, that means we found out that a parallelogram inscribed in a circle is rectangle.
Now let's talk about the trapezoid. What happens if a trapezoid is inscribed in a circle? But it turns out there will be isosceles trapezoid . Why?
Let the trapezoid be inscribed in a circle. Then again, but due to the parallelism of the lines and.
This means we have: → → isosceles trapezoid.
Even easier than with a rectangle, right? But you need to firmly remember - it will come in handy:
Let's list the most important ones again main statements tangent to a quadrilateral inscribed in a circle:
- A quadrilateral is inscribed in a circle if and only if the sum of its two opposite angles is equal to
- A parallelogram inscribed in a circle - certainly rectangle and the center of the circle coincides with the intersection point of the diagonals
- A trapezoid inscribed in a circle is equilateral.
Inscribed quadrilateral. Average level
It is known that for every triangle there is a circumscribed circle (we proved this in the topic “The Circumscribed Circle”). What can be said about the quadrilateral? It turns out that NOT EVERY quadrilateral can be inscribed in a circle, and there is such a theorem:
A quadrilateral is inscribed in a circle if and only if the sum of its opposite angles is equal to.
In our drawing -
Let's try to understand why this is so? In other words, we will now prove this theorem. But before you prove it, you need to understand how the statement itself works. Did you notice the words “then and only then” in the statement? Such words mean that harmful mathematicians have crammed two statements into one.
Let's decipher:
- “Then” means: If a quadrilateral is inscribed in a circle, then the sum of any two of its opposite angles is equal.
- “Only then” means: If a quadrilateral has two opposite angles whose sum is equal, then such a quadrilateral can be inscribed in a circle.
Just like Alice: “I think what I say” and “I say what I think.”
Now let’s figure out why both 1 and 2 are true?
First 1.
Let a quadrilateral be inscribed in a circle. Let's mark its center and draw radii and. What will happen? Do you remember that an inscribed angle is half the size of the corresponding central angle? If you remember, we’ll use it now, and if not, take a look at the topic "Circle. Inscribed angle".
Inscribed
Inscribed
But look: .
We get that if - is inscribed, then
Well, it’s clear that it also adds up. (we also need to consider).
Now “vice versa”, that is, 2.
Let it turn out that in a quadrilateral the sum of some two opposite angles is equal. Let's say let
We don't know yet whether we can describe a circle around it. But we know for sure that we are guaranteed to be able to describe a circle around a triangle. So let's do it.
If a point does not “sit” on the circle, then it inevitably ends up either outside or inside.
Let's consider both cases.
Let the point be outside first. Then the segment intersects the circle at some point. Let's connect and. The result is an inscribed (!) quadrilateral.
We already know about it that the sum of its opposite angles is equal, that is, and according to our condition.
It turns out that it should be so that.
But this cannot possibly be because - external corner for and means .
What about inside? Let's do similar things. Let the point be inside.
Then the continuation of the segment intersects the circle at a point. Again - an inscribed quadrilateral, and according to the condition it must be satisfied, but - an external angle for and means, that is, again it cannot be that.
That is, a point cannot be either outside or inside the circle - that means it is on the circle!
The whole theorem has been proven!
Now let's see what good consequences this theorem gives.
Corollary 1
A parallelogram inscribed in a circle can only be a rectangle.
Let's understand why this is so. Let a parallelogram be inscribed in a circle. Then it should be done.
But from the properties of a parallelogram we know that.
And the same, naturally, regarding the angles and.
So it turns out to be a rectangle - all the corners are along.
But, in addition, there is an additional pleasant fact: the center of the circle circumscribed about the rectangle coincides with the point of intersection of the diagonals.
Let's understand why. I hope you remember very well that the angle subtended by the diameter is a straight line.
Diameter,
Diameter
which means it is the center. That's all.
Corollary 2
A trapezoid inscribed in a circle is isosceles.
Let the trapezoid be inscribed in a circle. Then.
And also.
Have we discussed everything? Not really. In fact, there is another, “secret” way to recognize an inscribed quadrilateral. We will not formulate this method very strictly (but clearly), but will prove it only at the last level of the theory.
If in a quadrilateral one can observe such a picture as here in the figure (here the angles “looking” at the side of the points and are equal), then such a quadrilateral is inscribed.
This is a very important drawing - in problems it is often easier to find equal angles, than the sum of angles and.
Despite the complete lack of rigor in our formulation, it is correct, and moreover, it is always accepted by the Unified State Exam examiners. You should write something like this:
“- inscribed” - and everything will be fine!
Don't forget this one important sign- remember the picture, and perhaps it will catch your eye in time when solving the problem.
Inscribed quadrilateral. Brief description and basic formulas
If a quadrilateral is inscribed in a circle, then the sum of any two of its opposite angles is equal to
and vice versa:
If a quadrilateral has two opposite angles whose sum is equal, then the quadrilateral is cyclic. 
A quadrilateral is inscribed in a circle if and only if the sum of its two opposite angles is equal.
Parallelogram inscribed in a circle- certainly a rectangle, and the center of the circle coincides with the intersection point of the diagonals.
A trapezoid inscribed in a circle is isosceles.
For a triangle, both an inscribed circle and a circumscribed circle are always possible.
For a quadrilateral, a circle can be inscribed only if the sums of its opposite sides are the same. Of all the parallelograms, only a rhombus and a square can be inscribed with a circle. Its center lies at the intersection of the diagonals.
A circle can be described around a quadrilateral only if the sum of the opposite angles is 180°. Of all the parallelograms, only a rectangle and a square can be described as a circle. Its center lies at the intersection of the diagonals.
It is possible to describe a circle around a trapezoid, or a circle can be inscribed in a trapezoid if the trapezoid is isosceles.
Circumcenter
Theorem. The center of a circle circumscribed about a triangle is the point of intersection of the perpendicular bisectors to the sides of the triangle.
The center of a circle circumscribed about a polygon is the point of intersection of the perpendicular bisectors to the sides of this polygon.
Center Inscribed Circle
Definition. Inscribed in convex polygon a circle is a circle that touches all sides of that polygon (that is, each of the sides of the polygon is tangent to the circle).
The center of the inscribed circle lies inside the polygon.
A polygon into which a circle is inscribed is called circumscribed.
A circle can be inscribed in a convex polygon if bisectors of all of him internal corners intersect at one point.
Center of a circle inscribed in a polygon- the point of intersection of its bisectors.
The center of the inscribed circle is equidistant from the sides of the polygon. The distance from the center to any side is equal to the radius of the inscribed circle. According to the property of tangents drawn from one point, any vertex of the circumscribed polygon is equidistant from the tangent points lying on the sides extending from this vertex.
A circle can be inscribed in any triangle. The center of a circle inscribed in a triangle is called the incenter.
A circle can be inscribed in a convex quadrilateral if and only if the sum of its lengths opposing sides are equal. In particular, a circle can be inscribed in a trapezoid if the sum of its bases is equal to the sum of its sides.
A circle can be inscribed in any regular polygon. Around any regular polygon You can also describe a circle. The center of the incircle and circumcircle lie at the center of a regular polygon.
For any circumscribed polygon, the radius of the inscribed circle can be found using the formula
Where S is the area of the polygon, p is its semi-perimeter.
Regular n-gon - formulas
Formulas for the side length of a regular n-gon
1. Formula for the side of a regular n-gon in terms of the radius of the inscribed circle:
2. Formula for the side of a regular n-gon in terms of the radius of the circumscribed circle:
Formula for the incircle radius of a regular n-gon
Formula for the radius of the inscribed circle of an n-gon using the length of the side:
4. Circumcision radius formula regular triangle through side length:
6. Formula for the area of a regular triangle in terms of the radius of the inscribed circle: S = r 2 3√3
7. Formula for the area of a regular triangle in terms of the radius of the circumcircle:
4. Formula for the circumradius of a regular quadrilateral in terms of side length:
2. Side formula regular hexagon through the radius of the circumscribed circle: a = R
3. Formula for the radius of the inscribed circle of a regular hexagon in terms of the length of the side:
6. Formula for the area of a regular hexagon in terms of the radius of the inscribed circle: S = r 2 2√3
7. Formula for the area of a regular hexagon in terms of the radius of the circumscribed circle:
| S= | R 2 3√3 |
8. Angle between the sides of a regular hexagon: α = 120°
Number meaning(pronounced "pi") - mathematical constant, equal to the ratio
the circumference of a circle to the length of its diameter, it is expressed as an infinite decimal fraction.
Denoted by the letter "pi" of the Greek alphabet. What is pi equal to? IN simple cases It is enough to know the first 3 signs (3.14).
53. Find the length of the arc of a circle of radius R corresponding to the central angle of n°
The central angle subtended by an arc whose length is equal to the radius of the circle is called an angle of 1 radian.
The degree measure of an angle of 1 radian is:
Since the arc length π
R (semicircle), subtends central angle at 180 °
, then an arc of length R subtends the angle into π
times smaller, i.e. 
And vice versa
Because π = 3.14, then 1 rad = 57.3°
If the angle contains a radian, then it degree measure equal to 
And vice versa 
Usually, when denoting the measure of an angle in radians, the name “rad” is omitted.
For example, 360° = 2π rad, they write 360° = 2π
The table shows the most common angles in degrees and radians.
ENTER
ENTER
1. someone-what. Write down, enter, include in the list (official).
2. What. Attribute between, near what is written. Fill in the missing words.
3. What. Draw one figure inside another so that it is inscribed (in 2 values, mat.). Inscribe a triangle in a circle.
Ushakov's Explanatory Dictionary. D.N. Ushakov. 1935-1940.
Antonyms:
See what “ENTER” is in other dictionaries:
Write down, enter, enter. Ant. delete Dictionary of Russian synonyms. enter insert, enter, enter see also write down Dictionary of synonyms of the Russian language. Practical guide. M.: Russian language. Z. E. Alexandrova ... Synonym dictionary
ENTER, looking, looking; isan; Sovereign 1. whom (what) into what. Having written, enter, include where n. B. quotation in text. B. last name on the list. V. a glorious page in history (trans.; high). 2. what. In mathematics: draw one figure inside another with... ... Ozhegov's Explanatory Dictionary
enter- what's what. Fill in the missing word in the text. Who, in a moment of anger, did not demand from them [ stationmasters] fatal book, in order to write into it his useless complaint... (Pushkin) ... Control Dictionary
enter- ENTER, oh, oh; nesov. (owl. ENTER, I will enter, you will enter). 1. who goes where. Let them spend the night; sleep. 2. to whom, where. Hit, hit. Put a hook in his mouth (in his face) ... Dictionary of Russian argot
enter- I write/, write/sew; inscribed; san, a, o; St. see also enter, fit in, enter what 1) Insert what l. additionally to the already written text; make an insertion, a postscript between or near what is written, printed... Dictionary of many expressions
I owls trans. see enter I II owls. trans. see enter II Explanatory Dictionary of Efremova. T. F. Efremova. 2000... Modern Dictionary Russian language Efremova
Write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, write in, ... ... Forms of words
Write out, cross out... Dictionary of antonyms
enter- write in, write in, vp is looking... Russian spelling dictionary
enter- (I)‚ I’ll write/(s)‚ write/sesh(s)‚ joke(s)… orthographic dictionary Russian language
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Definitions
A circle \(S\) is inscribed in an angle \(\alpha\) if \(S\) touches the sides of the angle \(\alpha\) .
A circle \(S\) is inscribed in a polygon \(P\) if \(S\) touches all sides of \(P\) .
In this case, the polygon \(P\) is said to be circumscribed about a circle.
Theorem
The center of a circle inscribed in an angle lies on its bisector.
Proof
Let \(O\) be the center of some circle inscribed in the angle \(BAC\) . Let \(B"\) be the point of contact of the circle and \(AB\) , and \(C"\) be the point of contact of the circle and \(AC\) , then \(OB"\) and \(OC"\) – radii drawn to the points of tangency, therefore, \(OC"\perp AC\) , \(OB"\perp AB\) , \(OC" = OB"\) .
This means that the triangles \(AC"O\) and \(AB"O\) are right triangles, which have equal legs and a common hypotenuse, therefore, they are equal, whence \(\angle CAO = \angle BAO\), which is what needed to be proved.
Theorem
A single circle can be inscribed into any triangle, and the center of this inscribed circle is the point of intersection of the bisectors of the triangle.
Proof
Let's draw the bisectors of the angles \(\angle A\) and \(\angle B\) . Let them intersect at the point \(O\) .
Because \(O\) lies on the bisector \(\angle A\), then the distances from the point \(O\) to the sides of the angle are equal: \(ON=OP\) .
Because \(O\) also lies on the bisector \(\angle B\) , then \(ON=OK\) . Thus, \(OP=OK\), therefore, the point \(O\) is equidistant from the sides of the angle \(\angle C\), therefore, lies on its bisector, i.e. \(CO\) is the bisector of \(\angle C\) .
Thus, the points \(N, K, P\) are equidistant from the point \(O\), that is, they lie on the same circle. By definition, this is a circle inscribed in a triangle.
This circle is unique, because if we assume that there is another circle inscribed in \(\triangle ABC\), then it will have the same center and the same radius, that is, it will coincide with the first circle.
Thus, the following theorem was simultaneously proved:
Consequence
The bisectors of a triangle intersect at one point.
Circumscribed area theorem
If \(a,b,c\) are the sides of the triangle, and \(r\) is the radius of the circle inscribed in it, then the area of the triangle \where \(p=\dfrac(a+b+c)2\) is the semi-perimeter triangle.
Proof
\(S_(\triangle ABC)=S_(\triangle AOC)+S_(\triangle AOB)+S_(\triangle BOC)=\frac12OP\cdot AC+\frac12 ON\cdot AB+\frac12 OK\cdot BC\).
But \(ON=OK=OP=r\) are the radii of the inscribed circle, therefore,
Consequence
If a circle is inscribed in a polygon and \(r\) is its radius, then the area of the polygon is equal to the product of the half-perimeter of the polygon by \(r\) : \
Theorem
A circle can be inscribed in a convex quadrilateral if and only if the sums of its opposite sides are equal.
Proof
Necessity. Let us prove that if a circle is inscribed in \(ABCD\), then \(AB+CD=BC+AD\) .
Let \(M,N,K,P\) be the tangent points of the circle and the sides of the quadrilateral. Then \(AM, AP\) are segments of tangents to the circle drawn from one point, therefore, \(AM=AP=a\) . Likewise, \(BM=BN=b, \CN=CK=c, \DK=DP=d\).
Then: \(AB+CD=a+b+c+d=BC+AD\) .
Adequacy. Let us prove that if the sums of the opposite sides of a quadrilateral are equal, then a circle can be inscribed in it.
Let's draw the bisectors of the angles \(\angle A\) and \(\angle B\) , let them intersect at the point \(O\) . Then the point \(O\) is equidistant from the sides of these angles, that is, from \(AB, BC, AD\) . Let us inscribe a circle in \(\angle A\) and \(\angle B\) with center at point \(O\) . Let us prove that this circle will also touch the side \(CD\) .
Let's assume that this is not the case. Then \(CD\) is either a secant or does not have common points with a circle. Let's consider the second case (the first will be proved in a similar way).
Let's draw a tangent line \(C"D" \parallel CD\) (as shown in the figure). Then \(ABC"D"\) is a circumscribed quadrilateral, therefore, \(AB+C"D"=BC"+AD"\) .
Because \(BC"=BC-CC", \AD"=AD-DD"\) , then:
We found that in the quadrilateral \(C"CDD"\) the sum of the three sides is equal to the fourth, which is impossible*. Therefore, the assumption is false, which means that \(CD\) is tangent to the circle.
Comment*. Let us prove that in convex quadrilateral a side cannot be equal to the sum of the other three.
Because in any triangle, the sum of two sides is always greater than the third, then \(a+x>d\) and \(b+c>x\) . Adding these inequalities, we get: \(a+x+b+c>d+x \Rightarrow a+b+c>d\). Therefore, the sum of any three sides is always greater than the fourth side.
Theorems
1. If a circle is inscribed in a parallelogram, then it is a rhombus (Fig. 1).
2. If a circle is inscribed in a rectangle, then it is a square (Fig. 2).
The converse statements are also true: you can fit a circle into any rhombus or square, and only one.
Proof
1) Consider a parallelogram \(ABCD\) into which a circle is inscribed. Then \(AB+CD=BC+AD\) . But in a parallelogram opposite sides are equal, i.e. \(AB=CD, \BC=AD\) . Therefore, \(2AB=2BC\), which means \(AB=BC=CD=AD\), i.e. this is a rhombus.
The converse statement is obvious, and the center of this circle lies at the intersection of the diagonals of the rhombus.
2) Consider the rectangle \(QWER\) . Because the rectangle is a parallelogram, then according to the first point \(QW=WE=ER=RQ\), i.e. this is a rhombus. But because All its angles are right, then it is a square.
The converse statement is obvious, and the center of this circle lies at the intersection of the diagonals of the square.