📐 geometry

1. **Problem Statement:** Two circles with centers $O_1$ and $O_2$ each have radius $9$ cm and intersect. We need to find:

1. Problem 7: If the perimeter of a circle is equal to that of a square, find the ratio of their areas. 2. Formula:

1. **Problem Statement:** In trapezium ABCD with parallel sides AB and DC, where AB = 18 cm, DC = 32 cm, and the distance between AB and DC is 14 cm, arcs of radius 7 cm are drawn

1. **State the problem:** We are given that the perimeter (circumference) of a circle is equal to the perimeter of a square. We need to find the ratio of their areas.

1. **Problem statement:** We need to find the perimeter of trapezium ABCD with sides AB = 24 m, BC = 26 m, AD = 42 m, and angle at A and B are right angles. 2. **Understanding the

1. **State the problem:** We are given a triangle with angles \(\angle QTR = 140^\circ\), \(\angle QSR = 2x + 35^\circ\), and \(\angle TRS = 3x - 10^\circ\).

1. **Problem Statement:** Draw triangle $\Delta ABC$ with vertices $A(-3,5)$, $B(-6,3)$, and $C(-2,3)$.

1. **State the problem:** We have point A at coordinates $(1, 5)$ on the Cartesian plane. 2. **Translation rule:** To translate a point, add the horizontal shift to the $x$-coordin

1. **Problem statement:** We have quadrilateral LMNO with vertices L(3,2), M(5,1), N(6,2), and O(5,4). 2. **Transformation rule for 4.1.1:** The rule is $(x,y) \to (x+2, y-7)$.

1. **Problem Statement:** We have quadrilateral LMNO with vertices L(3, 2), M(5, 1), N(6, 2), and O(5, 4).

1. The problem asks to find the angle vertical to \(\angle 2\). 2. Vertical angles are the pairs of opposite angles made by two intersecting lines. They are always equal.

1. **Stating the problem:** We have a circular park with radius $r=14$ meters.

1. **Problem Statement:** Given a circle with center $O$ and points $A, B, C, D, E$ on the circumference such that $AC = AD$, $M$ is the midpoint of $AD$, and $OME$ is a straight l

1. **Постановка задачи:** Дана правильная четырёхугольная пирамида MABCD с основанием ABCD — квадратом. Сфера описана вокруг пирамиды так, что плоскость основания проходит через це

1. **Problem statement:** We have a row of $n$ cubes, each cube is $1 \text{ cm}$ on each side. We want to find:

1. **Problem statement:** We need to find the length of the hypotenuse in a right-angled triangle where the two legs measure 8 cm and 3.9 cm. 2. **Formula:** According to Pythagora

1. **Problem Statement:** We are given a right prism with a surface area of 132 cm\textsuperscript{2} and need to find the value of $x$. 2. **Understanding Surface Area of a Right

1. **State the problem:** Find the area of the compound figure composed of 4 connected rectangles forming a step-like shape with given dimensions. 2. **Identify the rectangles:**

1. **Problem Statement:** Given a circle with center $O$ and points $A$, $B$, $C$, and $D$ on the circumference, where $O$ lies on line segment $AB$. The angle $\angle DAB$ is $44^

1. **Problem statement:** A circle is inscribed inside a square such that the circle touches all four sides of the square. Given the area of the circle is 139.7 cm², find the area

1. **State the problem:** A circle is inscribed inside a square, touching all four sides. Given the area of the circle is 131.5 cm², find the length of the sides of the square. 2.