📐 geometry

1. **State the problem:** Find the radius of a circle given its circumference is 106.81 cm. 2. **Formula used:** The circumference $C$ of a circle is given by the formula $$C = 2\p

1. **Problem:** Find the area and circumference of a circle with diameter 16.6 meters. 2. **Formulas:**

1. **Problem 1:** Given a circle with center $O$, radius $OJ = 10$, and an intercepted arc $JK$ of $120^\circ$, find the length of chord $JK$. 2. **Formula:** The length of a chord

1. **State the problem:** Find the equation of the inscribed circle (incircle) of the triangle with vertices $A(-10,6)$, $B(10,8)$, and $C(0,-8)$. 2. **Recall the formula for a cir

1. **Problem Statement:** Determine the type of center represented by the black dot in triangle ABC where points D, E, and F are midpoints of sides AB, BC, and AC respectively, i.e

1. **State the problem:** We need to approximate the area of the air (shaded region) and the foul territory (nonshaded region) in a baseball stadium diagram where $H$ is home plate

1. **State the problem:** We have an ice hockey goal with height 1.22 m and width 1.83 m. A player stands at point P, with distances \(|PG|=3.5\) m, \(|PL|=4.9\) m, and \(|PR|=5.3\

1. **State the problem:** We have a circle with radius 4.57 m and a sector inside it defined by angle $\angle AOC = 2.17$ radians and radius $AO = OC = 3.36$ m. We need to find the

1. **Problem Statement:** Calculate the angle $\angle LQR$ in triangle $LQR$ where sides are given as $LQ=21.22$ m, $QR=19.63$ m, and $LR=1.83$ m. 2. **Formula Used:** To find an a

1. **State the problem:** We have a square with a perimeter of 72 meters and need to find its area. 2. **Recall the formulas:**

1. **State the problem:** Given parallelogram ABCD with diagonals AC and BD intersecting at E, prove that $AE \cong CE$ and $BE \cong DE$. 2. **Recall properties:** In a parallelog

1. **Stating the problem:** We want to find how many small tanks (each 4 ft by 4 ft) can be filled with the water from Part A. The small tank is a cube with side length 4 ft. 2. **

1. **State the problem.** We have a triangle with interior angles labeled $2x-10$, $4x$, and $3x-8$.

1. **Problem Statement:** Given two parallel lines AB and JK, and a transversal intersecting them, find the value of $x$ given the angles $y^\circ$, $(5x - 21)^\circ$, and $(2x - 9

1. **Problem 6: Find the lateral surface area of a triangular prism with an equilateral base of side 1.5 in and length 10 in.** 2. The lateral surface area (LSA) of a prism is the

1. **Problem Statement:** Given that lines KL and MN are parallel, and lines LM and NO are parallel, find the value of $x$ given the angles $3x^\circ$, $96^\circ$, and $2y^\circ$ i

1. **State the problem:** We have a circle with radius 4 units and a shaded sector of 270°. 2. **Formula for area of a sector:** The area $A$ of a sector with radius $r$ and centra

1. **State the problem:** Find the volume of the dollhouse, which consists of a rectangular prism base and a triangular prism roof. 2. **Formula for volume:**

1. **State the problem:** Find the radius of a cylinder with volume $V = 5070\pi$ cubic centimeters and height $h = 30$ centimeters. 2. **Formula for the volume of a cylinder:**

1. **Problem Statement:** Given two parallel lines $\ell \parallel m$ cut by a transversal, find the measure of angle $\angle QTP$ given the angles $3x^\circ$, $89^\circ$, and $(5x

1. **State the problem:** We need to find the measure of angle $\angle CEF$ given the angles around points $C$ and $E$ with expressions involving $x$ and $y$. 2. **Identify the giv