1103138706
Level:
A
In which of the pictures is the triangle \( A'B'C' \) the image of the equilateral triangle \( ABC \) in a point reflection in the point \( S \)?
A
1103138705
Level:
A
In which of the pictures is the circle \( k’ \) the image of the circle \( k \) in a point reflection in the point \( S \)?
1103138704
Level:
A
In the given pictures, there are letters \( F \) shown in different positions. Choose the picture that shows a letter \( F \) and its image in a point reflection in the point \( S \).
1103138703
Level:
A
Let \( ABCD \) be a rectangle and let \( M \) be a point, such that \( M\in BD \) and \( |BM|:|MD|=1:3 \).
Which of the pictures shows the rectangle \( A'B'C'D' \) which is the reflection of the original rectangle \( ABCD \) reflected in the point \( M \)?
1103138702
Level:
A
Let \( ABCD \) be a square and let \( M \) be a point, such that \( M\in AB \) and \(|AM|:|MB|=3:1 \).
Which of the pictures shows the square \( A'B'C'D' \) which is the reflection of the original square \( ABCD \) reflected in the point \( M \)?
1003138701
Level:
A
When reflecting in a point \( S \), which of lines are mapped to the same lines?
Every line passing through the point \( S \).
Every line that is not passing through the point \( S \).
There are no lines which are mapped to the same lines in a reflection in the point \( S \).
Only two mutually perpendicular lines passing through the point \( S \).
1103077102
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle circumscribed about a circle of radius \( r \).
\( 6\sqrt3 r \)
\( 2\sqrt3 r \)
\( \frac{2r}{\sqrt3} \)
\( \frac{6r}{\sqrt3} \)
1103077101
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle inscribed in a circle of radius \( r \).
\( 3\sqrt3 r \)
\( \sqrt3 r \)
\( 3 r \)
\( \frac{3\sqrt3 r}2 \)
1003023111
Level:
A
Select the set that contains measures of two angles that do not take the same position as the angle \( \alpha=\frac3{10}\pi \) radians on the unit circle.
\( \left\{ \frac{37}{10}\pi;\ -\frac{37}{10}\pi \right\} \)
\( \left\{ \frac{63}{10}\pi;\ -\frac{103}{10}\pi \right\} \)
\( \left\{ -\frac{17}{10}\pi;\ -\frac{77}{10}\pi \right\} \)
\( \left\{ -\frac{37}{10}\pi;\ \frac{23}{10}\pi \right\} \)
1003023110
Level:
A
Which of the given sets contains measures of three angles that take the same position as the angle \( \varphi = 18^{\circ} \) on the unit circle?
\( \left\{ 378^{\circ};\ -342^{\circ};\ -1422^{\circ} \right\} \)
\( \left\{ 1098^{\circ};\ 1818^{\circ};\ -1052^{\circ} \right\} \)
\( \left\{ 1098^{\circ};\ -1062^{\circ};\ -1812^{\circ} \right\} \)
\( \left\{ 378^{\circ};\ 1092^{\circ};\ -1062^{\circ} \right\} \)