📐 geometry

1. **Problem:** Find the angle corresponding to \(\angle BOC\) from the given options. 2. **Understanding the problem:** The problem involves identifying which angle is equal or co

1. **Problem Statement:** Show that if a chord subtends a 90° angle at a point on the circle, then the chord is a diameter. 2. **Key Concept:** The angle subtended by a chord at an

1. **Problem Statement:** We are given a triangular prism ABC.EFG with an equilateral triangle base ABC.

1. **Problem Statement:** Given a circle with center $N$ and two diameters $LA$ (vertical) and $CE$ (diagonal), and $m = 124^\circ$, find the measures of angles $\angle 1$ through

1. **Stating the problem:** We are given a parallelogram with a base length of 6 cm and an area of 18 cm². We need to find the height of the parallelogram. 2. **Formula used:** The

1. **State the problem:** Calculate the area of a parallelogram with base length $8$ cm and height $9$ cm. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. **State the problem:** We need to find the height of a trapezium given its area and the lengths of the two parallel sides. 2. **Formula:** The area $A$ of a trapezium is given b

1. **State the problem:** We need to find the area of a trapezium with top base $16$ cm, bottom base $8$ cm, and height $7$ cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** We need to find the area of a trapezium with parallel sides of lengths 5 cm and 30 cm, and a height of 12 cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** We have a right-angled triangle ABC with angle B as the right angle. Given lengths are $AB = 52.5$ cm and $AC = 59.5$ cm. We need to find the length $BC$.

1. **Problem Statement:** We have a triangle with side lengths 3 cm, 4 cm, and 4.5 cm. We need to find the radius of the circumcircle (উল্লাপকের বৃত্তের বাহর) and draw the circumci

1. **Problem:** Find the coordinates of point ب (B) in the coordinate plane. 2. **Given:** The graph shows point ب at coordinates (2, 1).

1. The problem is to find the coordinates of point A without using the BD equation. 2. To solve this, we need to understand what information is given about point A and the context

1. Problem: Find the ratio of areas of two squares with given side lengths. 2. Formula: The ratio of areas of two squares is the square of the ratio of their corresponding side len

1. **Problem Statement:** Given triangle ABC with vertices B(5,0), C(1,4), and A unknown. D is the midpoint of AC and lies on the y-axis. AE is the perpendicular bisector of BC and

1. Bài toán yêu cầu giải quyết mà không sử dụng tọa độ và vector. 2. Để giải các bài toán hình học phẳng mà không dùng tọa độ và vector, ta thường sử dụng các định lý hình học cổ đ

1. \textbf{Đề bài:} Cho hình vuông ABCD, trên cạnh BC lấy điểm M, AM cắt đường thẳng CD tại điểm N. Kéo dài DM cắt BN tại I. Chứng minh rằng CI vuông góc với AN. 2. \textbf{Phân tí

1. The problem describes a triangular region bounded by three lines: $x=1$, $y=2$, and $x+y=10$. 2. To understand the shape and find the vertices of the triangle, we find the inter

1. **Problem:** Find the largest volume of a cube that can be enclosed in a sphere of diameter 2 cm. 2. **Understanding the problem:** The cube is inscribed inside the sphere, so t

1. **Problem statement:** We have two identical rectangular prisms, each with height $90$ cm and a square base with side length $s$ cm. Each prism has surface area $K$ cm$^2$. When

1. **Problem:** Find the side length of a rhombus given its diagonals are 30 cm and 16 cm. 2. **Formula:** The diagonals of a rhombus bisect each other at right angles. Each side $