📐 geometry

1. **State the problem:** Find the area of a circle given its radius. 2. **Formula:** The area $A$ of a circle with radius $r$ is given by the formula:

1. **Stating the problem:** We want to find the side length of a cube that can be inscribed inside a sphere with radius $\frac{3\sqrt{3}}{2}$.\n\n2. **Formula and explanation:** Wh

1. **State the problem:** We have a right triangle ABC with a right angle at C, angle A is 65 degrees, hypotenuse AB is 7 units, and we need to find the length of side AC. 2. **For

1. The problem asks us to identify which shapes among A, B, C, and D are polygons. 2. A polygon is a closed plane figure with straight sides. It must have at least three straight s

1. **Nêu bài toán:** Cho đường tròn $(O; R)$ và điểm $A$ nằm ngoài đường tròn. Từ $A$ vẽ hai tiếp tuyến $AB$ và $AC$ với $B$, $C$ là các tiếp điểm. Đường thẳng $AO$ cắt $BC$ tại $H

1. **Problem Statement:** In a rectangle ABCD, the diagonals AC and BD intersect at O. Given that $\angle BOC = 40^\circ$, find $\angle OBC$ and $\angle OCB$. 2. **Important Proper

1. **Problem a:** Find the measures of the numbered angles in the isosceles trapezoid with one angle given as 66°. 2. **Step 1:** Recall that in an isosceles trapezoid, the base an

1. **State the problem:** Find the area of the polygon with vertices P, Q, R, S, M, N given the side lengths and right angles. 2. **Analyze the shape:** The polygon can be decompos

1. The problem asks: What is length and width? 2. Length and width are terms used to describe the dimensions of a two-dimensional shape, such as a rectangle.

1. **Problem Statement:** Compute the area enclosed by a straight line and a curve given the ordinates at intervals of 7.5 m using the Mid-ordinate rule, Trapezoidal rule, and Simp

1. **State the problem:** We have a cylinder net with two circular bases each of radius 5 mm and a rectangular side with height 4 mm and unknown length $x$. We need to find $x$ and

1. **Stating the problem:** Calculate the area of each room and the total area based on the given dimensions and shapes. 2. **Formula used:** The area of a rectangle is given by th

1. **Stating the problem:** We have a convex polygon where the sum of all interior angles except one is 2200⁰. We need to find the excluded interior angle. 2. **Formula for sum of

1. **State the problem:** We need to find the measure of angle $\angle GKL$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the relations

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \( (89 - 6x)^\circ \) and \( (3x + 62)^\circ \). We need t

1. The problem is to find the length of the hypotenuse $x$ in a right-angled triangle where the other two sides are 12 and 16. 2. We use the Pythagorean Theorem which states:

1. The problem is to find the length of the hypotenuse $x$ in a right triangle where the legs are 6 and 8. 2. We use the Pythagorean Theorem which states: $$x^2 = a^2 + b^2$$ where

1. **Problem statement:** Three identical circles each with radius 2 intersect at a common point. The centers of the circles form an equilateral triangle. Inside the overlapping re

1. The problem is to find the surface area, and you mentioned you got 95.13 as the answer. 2. Surface area depends on the shape. For example, for a sphere, the formula is $$SA = 4\

1. **Problem Statement:** Calculate the volume and surface area of a composite solid consisting of a cylinder on top of a cuboid base.

1. **State the problem:** Linda runs along the path A to B to D to C to A around a rectangular field. We need to find the total distance she runs. 2. **Identify the sides of the re