📐 geometry

1. **State the problem:** We are given a cylinder with a radius of 7 cm and a total surface area of 572 cm². We need to find its height. 2. **Recall the formula for the surface are

1. **State the problem:** We have an isosceles trapezium with the shorter parallel side on top and the longer parallel side on the bottom. The bottom interior angles are each 60°.

1. نبدأ بتحديد المشكلة: لدينا نقطة A بإحداثيات (5, -2) ونقطة B بإحداثيات (4, -7). النقطة Q تقع على القطعة المستقيمة AB بحيث طول AQ يساوي ثلثي طول AB. 2. نحسب متجه AB:

1. نبدأ ببيان المشكلة: لدينا مثلث قائم الزاوية مع ضلعين طولهما 2 متر، والوتر طوله 3 متر، وزاوية 45 درجة عند النقطة A. 2. نلاحظ أن المثلث قائم الزاوية والوتر 3 متر، والزاوية 45 درجة

1. The problem states that a triangle has interior angles measuring $2c - 9^\circ$, $3c + 5^\circ$, and $c^\circ$. We need to find the value of $c$. 2. According to the Triangle An

1. **State the problem:** We have a triangle with three interior angles: $x + 11^\circ$, $5x$, and $x + 11^\circ$. We need to find the value of $x$. 2. **Recall the Triangle Angle-

1. **State the problem:** We have a triangle with three angles labeled as follows: - Top-left angle: $2a + 20^\circ$

1. The problem states that the three angles of a triangle are given as $2u + 7^\circ$, $3u + 4^\circ$, and $2u - 4^\circ$. We need to find the value of $u$. 2. Recall that the sum

1. **State the problem:** We are given a triangle with three interior angles: $2v + 11^\circ$, $2v - 16^\circ$, and $34^\circ$. We need to find the value of $v$. 2. **Recall the Tr

1. **State the problem:** We have a triangle with three angles: 34°, $2a - 32°$, and $2a - 46°$. We need to find the value of $a$. 2. **Recall the Triangle Angle-Sum Theorem:** The

1. **State the problem:** We have a triangle with three angles: $2c + 23^\circ$, $65^\circ$, and $2c$. We need to find the value of $c$. 2. **Recall the Triangle Angle-Sum Theorem:

1. **State the problem:** We have a triangle with angles $49^\circ$, $2a - 45^\circ$, and $2a$. We need to find the value of $a$. 2. **Recall the Triangle Angle-Sum Theorem:** The

1. **Problem statement:** Given a circle with center O, OA = 5 cm (radius), AB = 12 cm, and AB and BC are tangents to the circle at points A and C respectively.

1. Let's clarify the problem: You asked "How is the hole a cylinder?" which suggests you want to understand why a hole can be considered a cylindrical shape. 2. A cylinder is a 3D

1. **State the problem:** We have a rectangular block with dimensions 15 cm by 8 cm by 6 cm.

1. Problem statement: In triangle ABC a line intersects sides AB and AC at D and E respectively and is parallel to BC. 2. Goal: Prove that $\frac{AD}{AB} = \frac{AE}{AC}$.

1. **State the problem:** We have two similar right triangles. The first triangle has legs 2 and 3, and the second triangle has one leg 5 and the other leg labeled $x$. We need to

1. The problem states that two triangles are similar, meaning their corresponding sides are proportional. 2. The first triangle has sides 2, 3, and 5. The second triangle has sides

1. **State the problem:** We are given points A(-1,1,2), B(-1,3,0), C(1,1,3), and D(3,3,5) in 3D space. We need to determine if (a) the volume of tetrahedron ABCD is 2, (b) the poi

1. Let's state the problem: We want to find a simpler formula to calculate the height of a small cone. 2. Assume the small cone is similar to a larger cone, meaning their correspon

1. **State the problem:** We have a large cone with height 15 cm and base radius 6 cm. Inside it, a smaller similar cone with base radius $x$ cm is removed, creating a frustum. The