📐 geometry

1. The problem is to understand how to draw internal and external tangents to two circles. 2. First, let's define the terms:

1. **Problem:** In triangle ABC, given that \(\angle A = \angle B = 62^\circ\), find \(\angle C\). 2. **Formula:** The sum of the interior angles of any triangle is always \(180^\c

1. **State the problem:** We need to find the length of the hypotenuse $F$ of a right triangle with legs measuring 34 and 36 units. 2. **Formula used:** According to the Pythagorea

1. **State the problem:** We have an isosceles triangle ABC with sides BA = BC, angle BAC = 70°, and a circle inscribed inside the triangle with radius 6 cm. The length BO = 17.54

1. **State the problem:** We are given two right triangles with legs labeled as follows: the first triangle has legs $2x - 4$ and $39$, and the second smaller triangle has legs $x

1. **Find the distance between the points (-2, 0) and (4, 5).** The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

1. The first problem describes a right rectangular parallelepiped with height 6 units and vertex $D_1(4,5,0)$. We need to find the coordinates of the other vertices. 2. Since $D_1$

1. The problem asks: Which of the following is a regular polygon? 2. A regular polygon is defined as a polygon with all sides equal in length and all interior angles equal.

1. **Stating the problem:** We are given two quadrilaterals: one is a square and the other is a rectangle. We need to determine which statement about these two figures is true. 2.

1. The problem asks which figures have perpendicular sides. 2. Perpendicular sides meet at a right angle (90 degrees).

1. The problem asks which figures have perpendicular sides. 2. Perpendicular sides meet at a right angle (90 degrees).

1. **Problem statement:** We are given a triangle with sides 102 cm, 91.8 cm, and 100.2 cm, and we need to find the measure of the angle $\theta$ opposite the side of length 100.2

1. **State the problem:** We are given a triangle with angles expressed as algebraic expressions: $5x - 11$, $2x + 20$, and $11x - 63$. We need to solve for $x$ and then find the m

1. **Problem Statement:** Calculate the surface area of a triangular pyramid with given edge lengths: 12 cm, 8 cm, 6.9 cm, and 8 cm.

1. **State the problem:** We need to find the area of triangle $\triangle ABC$ with sides $AB=44$ km, $BC=48$ km, and $AC=39$ km using Heron's formula. 2. **Heron's formula:** The

1. Given $m \angle 2 = 50$, we need to find $m \angle 3$. 2. From the diagram, $\angle 2$ and $\angle 3$ are vertical angles, which means they are equal.

1. The problem asks to name the pairs of congruent and adjacent sides in a kite. 2. In a kite, two pairs of adjacent sides are congruent. This means each pair shares a common verte

1. **State the problem:** We are given a circle with center O and two arcs: $m\angle JR = 65.1^\circ$ and $m\angle FL = 21.4^\circ$. We need to find the measure of the exterior ang

1. **بيان المسألة:** لدينا ثلاث نقاط A، B، C ليست في استقامة.

1. **State the problem:** We are given a circle with center A and points L, B, Q, G, and M on or around the circle. We know the measures of angles $\angle MLG = 20.45^\circ$ and $\

1. **Problem Statement:** Determine the length of cylinder CB in the given mechanical diagram where angles are 90°, 25°, and 55°. 2. **Understanding the problem:** The points A, C,