📐 geometry

1. **State the problem:** We have a rectangular land with perimeter 170 m, length 15 m more than width, divided into three parts P, Q, and R. We need to find the area of the larges

1. **State the problem:** We have a circle $C_1$ with diameter endpoints $A(-2,18)$ and $B(14,6)$. We need to find the equation of $C_1$.

1. **Problem statement:** We have a circle $C_1$ with diameter endpoints $A(-2,18)$ and $B(14,6)$. We need to find the equation of $C_1$. Then, given another circle $C_2$ centered

1. **State the problem:** We need to find the length of segment $LW$ in a right triangle $LYW$ where $LY = 3.5$ units and $AY = 7.0$ units, with $A$ on $LY$ and $AY$ perpendicular

1. **Problem statement:** We have an isosceles triangle $\triangle FOR$ with $FO = 7.0$ units, $FR = 10.0$ units, and $OR = 11.2$ units. Segment $OR$ is parallel to segment $AN$. W

1. **Problem Statement:** We are given a circle with diameter \(\overline{AB}\) and points \(C\) and \(D\) on the circle. The angle between radii \(PA\) and \(PD\) is \((7x+1)^\cir

1. **Problem Statement:** We are given a circle with center $P$ and two diameters $\overline{AD}$ and $\overline{BE}$. We need to find the value of $k$ given the angle $\widehat{CA

1. **Problem Statement:** Find the length of side AB in a right triangle \(\triangle ABC\) where \(\angle B = 90^\circ\), hypotenuse \(AC = 25\) cm, and one leg \(BC = 24\) cm.

1. **Problem statement:** Calculate the area of trapezium ABCD where:

1. **Problem statement:** We have a right triangle GHD with a right angle at H. The hypotenuse GD is 18 units, side GH is 14 units, and we need to find the length HD. 2. **Identify

1. **Stating the problem:** We need to find the area of a trapezium (trapezoid) with given side lengths and angles. 2. **Given data:**

1. **Problem Statement:** Define the four boundary lines of a recreational park given its coordinates and label them on a coordinate grid. 2. **Understanding Boundary Lines:** Boun

1. The problem is to find the coordinates of the recreational area. 2. Since the problem statement is incomplete and does not provide any specific information or data about the rec

1. Problem: Find the length of the hypotenuse in a right triangle using the Pythagorean theorem. 2. The Pythagorean theorem states that in a right triangle, the square of the hypot

1. The problem states that $R$ is the radius of a circle. 2. The radius $R$ is the distance from the center of the circle to any point on its circumference.

1. The problem is to understand what the big $R$ and small $r$ represent in the context of circles. 2. In geometry, when dealing with circles, the letter $R$ often denotes the radi

1. The problem is to understand what the symbol $h$ means in the context of a trapezoid (trapezium). 2. In geometry, a trapezoid is a quadrilateral with at least one pair of parall

1. **State the problem:** We have two triangles with vertical segments inside them. We need to find the value of $x$ and then calculate the length of segment $VT$ in the second tri

1. **Problem Statement:** We have two similar triangles, $\triangle ABC$ and $\triangle BDE$. We know $DE=10$ cm, and the side lengths at vertices are $AB=6$, $BC=8$, and $AC=5$. W

1. **Problem Statement:** We are given two similar triangles, $\triangle ABC$ and $\triangle BDE$. We need to determine if the areas of $\triangle ABL$ and $\triangle ALC$ are equa

1. **Problem Statement:** We have a cyclic quadrilateral ABCD inscribed in a circle with diagonals AC and BD intersecting at point E. Given angles \(\angle A = 25^\circ\) and \(\an