📐 geometry

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.

1. **State the problem:** We need to find the circumference of a circle given its area is 130.1 cm². 2. **Recall the formulas:**

1. Calculate the circumference of a circle given its area 130.1 cm². The area of a circle is given by the formula $$A = \pi r^2$$ where $r$ is the radius.

1. Calculate the circumference of a circle given its area 130.1 cm². The area of a circle is given by the formula $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** We need to find the circumference of a circle given its area is 127.6 cm², rounded to three significant figures. 2. **Recall the formulas:**

1. **State the problem:** We need to find the circumference of a circle given its area is 127.6 cm². 2. **Recall the formulas:**

1. সমস্যাটি হলো: কেন্দ্রীয় বৃত্তের ব্যাস AB এবং বৃত্তং চতুর্ভুজ ABCD দেওয়া আছে, যেখানে \(\angle ABC = 65^\circ\) এবং \(\angle DAC = 40^\circ\)। আমাদের \(\angle BCD\) এর মান নির্ণ

1. **State the problem:** We need to find the radius $r$ of a circle given its area $A = 98.3$ cm$^2$. 2. **Formula used:** The area of a circle is given by the formula $$A = \pi r

1. **Stating the problem:** We have a rectangle with height equal to the diameter of a circle inside it, and the length of the rectangle is three times its height. We want to find