📐 geometry

1. **Problem Statement:** Calculate the size of angle $\hat{O}_1$ given that $O$ is the center of circle $HEATR$, $AOF$ is parallel to $EH$, $\hat{F}_2 = 60^\circ$, and $\hat{R}_1

1. **Problem statement:** We have a circle with center C and a chord of length 5.4 units subtending a 150° angle at the center. We need to show that the radius $r$ of the circle is

1. **State the problem:** We need to find the volume of a miniature globe with a diameter of 20 cm. 2. **Formula used:** The volume $V$ of a sphere is given by the formula:

1. **Stating the problem:** We have two parallel lines $l \parallel j$ cut by a transversal $m$. We need to find the values of angles $y$ and $x$ given that one angle is $67^\circ$

1. **State the problem:** We need to find the volume of a sphere with radius $r=9$ cm. 2. **Formula:** The volume $V$ of a sphere is given by the formula:

1. **State the problem:** We need to find the volume of a sphere with radius $r=9$ cm. 2. **Formula:** The volume $V$ of a sphere is given by the formula:

1. **State the problem:** We are given two angles around point K: $\angle JKL = (12x + 3)^\circ$ and $\angle KLM = (6x - 3)^\circ$. We know $\angle JKL$ is a right angle, so it mea

1. **Problem statement:** We are given two angles at point R on a straight line: one angle measures $3x$ degrees and the other measures $9x$ degrees. We need to find the value of $

1. **Problem Statement:** We analyze translations and rotations of given figures on a coordinate plane.

1. **Stating the problem:** We are given several pairs of angles formed by rays originating from point C. We need to analyze these pairs based on the given geometric configuration.

1. The problem involves understanding the geometric description of a rectangular chip with a gold-colored pattern on a card. 2. The chip is rectangular with rounded corners, positi

1. **Problem 1:** Given $BD \perp AB$, $BD \perp DE$, and $BC \cong DC$, prove $\angle A \cong \angle E$. 2. **Problem 2:** Given $BC \cong DC$, $AC \cong EC$, prove $\triangle ABC

1. **Problem 1:** Given $BD \perp AB$, $BD \perp DE$, and $BC \cong DC$, prove $\angle A \cong \angle E$. 2. **Problem 2:** Given $BC \cong DC$, $AC \cong EC$, prove $\triangle ABC

1. **Problem Statement:** We are given triangle MNP with incenter C. We know the length of side MP is 11, angle M is 20°, angle N is 30°, and segment CN (from vertex N to incenter

1. **Stating the problem:** We have a triangle with a side of length 12 cm opposite angle $\theta$, an adjacent angle of 16°, and a hypotenuse of 27 cm. We want to find the value o

1. The problem asks for the area of a rectangular pan with dimensions 9 inches by 13 inches. 2. The formula for the area $A$ of a rectangle is:

1. **State the problem:** Reese's old bike mirror is a rectangle with length 10 cm and width 5 cm. She wants a new circular mirror with approximately the same area. 2. **Formula fo

1. **State the problem:** We need to find the area of a circle with a diameter of 16 feet. 2. **Formula for the area of a circle:**

1. **Problem Statement:** We need to find the area of a sand mandala shaped like a circle with radius $r = 2$ ft. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We need to find the area $A$ of a circle with radius $r = 0.5$ meters using the formula $A = \pi r^2$. 2. **Formula and explanation:** The area of a circl

1. The problem is to find the area of a given shape or figure. 2. To find the area, we need to know the type of shape (e.g., rectangle, triangle, circle) and the relevant dimension