📐 geometry

1. **Nêu bài toán:** Cho đường tròn $(O; R)$ và điểm $A$ nằm ngoài đường tròn. Từ $A$ kẻ tiếp tuyến $AB$, $AC$ với tiếp điểm $B$, $C$. Gọi $H$ là giao điểm của $BC$ và $OA$. Kẻ đườ

1. **State the problem:** We need to find how much carpet is required to cover the surface of a cube with edge length 40 cm. 2. **Formula used:** The surface area $A$ of a cube wit

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 5, 5, and base 6 units, height of the triangle 4 units, and pri

1. The problem is to find the hypotenuse of a right-angled triangle given the lengths of the base and perpendicular sides. 2. The formula used is the Pythagorean theorem: $$\text{H

1. **Problem statement:** Given that lines $m$ and $n$ are parallel, and line $q$ is perpendicular to line $p$, with $m \angle 9 = 40^\circ$, find $m \angle 7$. 2. **Relevant facts

1. **Problem Statement:** We have two parallel lines cut by a transversal. Given that $m \angle 1 = 76^\circ$, find $m \angle 6$ and $m \angle 8$. 2. **Key Concepts:** When two par

1. **State the problem:** We have a triangular prism with a triangular base where one side is 15 cm and the height of the triangle is 8 cm. The volume of the prism is given as 720

1. **State the problem:** We are given the volume of a cube as 1728 cubic inches and need to find the side length in inches. 2. **Formula:** The volume $V$ of a cube with side leng

1. **State the problem:** We need to find the volume of a rectangular prism made up of unit cubes arranged in a 5 by 4 by 3 configuration. 2. **Formula for volume of a rectangular

1. **הבעיה:** נתון משולש ישר זווית $ABC$ עם זווית ישרה ב-$A$ ($\angle BAC=90^\circ$). נקודה $A(-2,0)$ על ציר ה-$x$, נקודה $E(4,9)$ היא אמצע הצלע $AB$. יש למצוא את נקודות $B$ ו-$C$,

1. **State the problem:** Find the volume of a triangular prism with a triangular base of base length 12 cm and height 8 cm, and prism length 20 cm. 2. **Formula:** The volume $V$

1. **הבעיה:** נתון משולש ישר זווית ABC עם \(\angle BAC = 90^\circ\), נקודה A ב-\(x\) ציר, נקודה E אמצע הצלע AB, \(A(-2,0)\), \(E(4,9)\). יש למצוא את שיעורי הנקודה B, שיפוע AB, משוו

1. **State the problem:** Find the volume of a triangular prism with a right triangle base having legs of 5 cm and 2 cm, and a prism length of 8 cm. 2. **Formula:** The volume $V$

1. **State the problem:** We need to find the volume of a rectangular cereal box with dimensions 12 inches (height), 8 inches (width), and 3 inches (depth). 2. **Formula for volume

1. The problem asks whether the "L" shaped non-shaded region counts or not. 2. To clarify, in geometry or area problems, shaded and non-shaded regions are often distinguished to sp

1. **Problem statement:** We have a large square ABCD with side length $5$ (since $1 + 3 + 1 = 5$). Inside it, three smaller squares are drawn with side lengths $1$, $3$, and $1$ a

1. **State the problem:** We need to find the radius of a cylinder given its volume and height. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$

1. **Stating the problem:** We have two large triangles sharing a common base of length 10 cm. The left triangle has height 7 cm, and the right triangle has height 12 cm.

1. **Problem statement:** We are given two triangles with angles and sides, and we need to solve for $x$ in the second triangle. 2. **Identify known angles and sides:**

1. **State the problem:** We are given two triangles VWU and YZX with some side lengths and angles, and we need to find the length of side YZ. 2. **Given data:**

1. Problem 6: Determine angle C in a right triangle with sides CB = 5 cm, CA = 13 cm, and angle B = 90°. 2. Use the Pythagorean theorem to find side AB: