📐 geometry

1. **Problem statement:** Given rectangle ABCD with diagonal BD, trace lines D₁ and D₂ perpendicular to BD at points A and C respectively.

1. The problem is to draw a combined figure of a cylinder and a cone. 2. A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.

1. **Problem statement:** Given two sides of a triangle with lengths 5.7 cm and 7.5 cm, and the angle opposite the side of length 7.5 cm is 105 degrees, find the unknowns of the tr

1. The problem is to find the area of plane shapes. 2. The formula for the area depends on the shape. For example, for a rectangle, the area $A$ is given by:

1. **State the problem:** We are given a right triangle $PQR$ with right angle at $R$. A perpendicular segment $TR$ is drawn from $R$ to $PQ$, forming two right angles at $T$ and $

1. The problem asks for the volume of a right rectangular pyramid with base length 12 feet, base width 9 feet, and height 18 feet. 2. The formula for the volume $V$ of a right rect

1. **Problem statement:** Given a circle with center O and two chords forming two angles on the circumference, one angle is 100° and the other is $x^\circ$. We need to find the val

1. **Problem Statement:** Given two parallelograms ABCD and ABEF standing on the same base AB and between the same parallel lines AB and FC, prove that the area of ABCD equals the

1. **Énoncé du problème :** Soit un triangle ABC non isocèle avec des points P sur la demi-droite [BA) et Q sur la demi-droite [CA) tels que $BP = CQ$ et $P \neq B$.

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).