📐 geometry

1. **State the problem:** We have a circle with radius $r$ and points $A$, $F$, $O$, $B$, and $G$ arranged such that $\triangle ABO$ and $\triangle GOF$ are right triangles inside

1. **Stating the problem:** We are given three line segments/rays OP, QR, and MN intersecting at the center. We need to determine which statement is true among: - OP is perpendicul

1. **State the problem:** We need to find the circumference of a circle with radius $r=2$ feet. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find the area of a circle with radius $r=5$ kilometers. 2. **Formula for the area of a circle:**

1. **State the problem:** Determine if triangles MNO and XYZ are similar and write a similarity statement if they are. 2. **Given information:** Triangle MNO has a right angle at N

1. **State the problem:** Pearl places a mirror 45 feet from the base of a building. She stands 12 feet from the mirror and can see the top of the building in the mirror. Pearl's h

1. **Problem a:** Given right triangle G T M with right angle at G, side G T = 33.4 m (vertical), diagonal T M = 48.2 m, and angle $x^\circ$ at M between G M and T M. Find $x$. 2.

1. **State the problem:** Calculate the tangent of the indicated angle $A$ in the right triangle where the vertical leg (opposite to angle $A$) is $4\sqrt{3}$ ft and the horizontal

1. **Problem:** Can you draw a circle and show its radius? 2. **Formula:** The radius is the distance from the center to the edge of the circle.

1. **Problem:** How do you find the radius of a circle, and can you show an example? 2. **Formula:** The radius is half of the diameter.

1. **State the problem:** We have two intersecting lines forming vertical angles. One angle is labeled $6x^\circ$, and the adjacent angle is labeled $(x - 2)^\circ$ which is also $

1. **Problem:** Given parallelogram ABCD with $m\angle D = x$ and $m\angle A = 3x + 4$, find $x$. 2. **Formula and rules:** In a parallelogram, opposite angles are congruent and co

1. **State the problem:** We need to find the image of square JKLM after a dilation centered at the origin with a scale factor of $\frac{1}{5}$. The original vertices are $J(-5,0)$

1. **State the problem:** We need to find the image of triangle \(\triangle EFG\) after a dilation centered at the origin with scale factor \(\frac{1}{5}\). The original vertices a

1. **State the problem:** We need to find the image of rectangle RSTU after a dilation centered at the origin with a scale factor of $\frac{1}{5}$. The original vertices are $R(-10

1. **State the problem:** Given two parallel lines $m \parallel n$, and the measure of angle $\angle 3 = 58^\circ$, find the measure of angle $\angle 7$. 2. **Recall the properties

1. **State the problem:** Given two parallel lines $m \parallel n$, and the measure of angle $\angle 3 = 58^\circ$, find the measure of angle $\angle 7$. 2. **Recall the properties

1. **State the problem:** We need to find the measure of arc $MO$ from the given picture. 2. **Identify the relevant information:** Since the picture is not provided here, typicall

1. **Problem statement:** Given a circle with center $L$, points $J$, $K$, $M$, and $P$ on the circle, segment $JK$ passes through $N$ and is perpendicular to segment $ML$ at $N$.

1. **State the problem:** We have two triangles, GHI and G'H'I', where G'H'I' is a dilation of GHI. We need to find the scale factor of the dilation. 2. **Recall the formula for sc

1. **State the problem:** We are given two triangles, UVW and U'V'W', where U'V'W' is a dilation of UVW. We need to find the scale factor of the dilation. 2. **Recall the formula f