📐 geometry

1. **State the problem:** We have a circle with area 144 cm². A chord is drawn 6 cm from the center, dividing the circle into two segments. We need to find the area of the smaller

1. **State the problem:** We are given the area of a rectangle as 160 m² and the breadth as 32 m. We need to find the length. 2. **Recall the formula for the area of a rectangle:**

1. **State the problem:** We need to find the number of sides of a regular polygon given that its exterior angle is \(\frac{1}{3}\) of its supplement. 2. **Recall definitions:**

1. **State the problem:** We have a point outside a circle from which a tangent and a secant are drawn.

1. **Problem Statement:** Find the area of the cross section of a right prism where the cross section is a triangle with base BC and height AB.

1. **Problem:** AB is the diameter of a circle and AC is its chord such that $\angle BAC = 30^\circ$. The tangent at C intersects AB extended at D. Prove $BC = BD$. Step 1: Since A

1. The problem states we have a right triangle with angles 90°, 36°, and a missing angle $l$. 2. The sum of angles in any triangle is always $180^\circ$.

1. **State the problem:** We are given a point $P = (1,4,c)$ in 3D space and a line $r$. We want to find the length of the perpendicular from $P$ to the line $r$ and show that the

1. The problem is to plot the points (1,0), (0,3), (-1,4), and (-5,-2) on graph paper and join them in order. 2. First, identify each point on the coordinate plane:

1. **State the problem:** We need to find the area of a polygon composed of a rectangle and a triangle on top. The rectangle has a height of 18 cm, and the triangle has a height of

1. **State the problem:** We have a square garden with an area of 140 m². We need to find: a) The approximate side length of the garden.

1. **State the problem:** We have a square garden with an area of 140 m². We need to find: a) The approximate side length of the garden.

1. **State the problem:** We have a shape ABCD enlarged by a scale factor of $-4$ with center of enlargement at $(1, 2)$ to get shape A'B'C'D'. Given coordinates of A' and B', find

1. **Problem statement:** We are given a parallelogram ABCD where the sum of the squares of two adjacent sides is $|AB|^2 + |AD|^2 = 12$. We need to find the sum of the squares of

1. **State the problem:** Given rectangle ABCD with sides AB = 5 in, BC = 12 in, CD = 5 in, DA = 12 in, and diagonals AC and BD intersecting at E. 2. **Find BD:** In a rectangle, d

1. **Problem 1: Find each length in rectangle ABCD** Given:

1. **Énoncé du problème :** Soit un triangle ABC avec E sur [AB] et F sur [AC]. Une parallèle à (BF) passant par E coupe [AC] en N.

1. **State the problem:** We are given a right triangle with vertices on the coordinate axes and need to find the range of the hypotenuse length based on the given points. 2. **Ide

1. **Problem statement:** Find the length of the tangent from a given point to each circle. The length of the tangent from a point $(x_1,y_1)$ to a circle with equation $$Ax^2 + Ay

1. **State the problem:** We have a right triangle ABC with legs $a$ and $b$, hypotenuse $h$, and area 25 m². We want to express $h$ in terms of the perimeter $P$. 2. **Recall the

1. Problema 1: Calcular el área lateral de un prisma regular con altura 6 cm y base hexagonal con lado 1.5 cm. 2. El área lateral de un prisma es el perímetro de la base por la alt