📐 geometry

1. The problem is to find the equation of a circle given its center and radius. 2. The general formula for a circle with center $(h, k)$ and radius $r$ is:

1. **Stating the problem:** We are given two parts: 5.a with an angle of 41° and 5.b with chord AB = 110°.

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula for a circle's equation:** The standard form is $$ (x - h)^2

1. **Stating the problem:** We have two separate geometry problems involving angles in circles.

1. **Problem Statement:** Identify the center and scale factor of a dilation and correct any errors in the student's identification.

1. **Problem statement:** We are given two vertices of a rectangular park at coordinates $(-3,5)$ and $(-3,-4)$, and we need to find the area of the park in square kilometers. 2. *

1. The problem asks for the coordinates of the points A and B plotted on the coordinate plane. 2. From the graph and the problem statement, point A is located at 4 units to the rig

1. **Problem:** Find the area of the trapezoid with bases 24.3 cm and 9.7 cm, and height 8.5 cm. 2. **Formula:** The area $A$ of a trapezoid is given by

1. **State the problem:** We need to find the coordinates of a point after reflecting it across the x-axis and then the y-axis (or vice versa).

1. **State the problem:** We need to find how many truckloads are required to move a conical pile of pebbles. The pile has a height of 10 yards and a base diameter of 6 yards. Each

1. **State the problem:** We have a point marked at coordinates $(-6,4)$ on a figure. We need to translate the figure 7 units down and find the new coordinates of the marked point.

1. **State the problem:** Prove that triangles $\triangle DEG$ and $\triangle FEG$ are congruent given that they are right triangles, $DG \cong FG$, and they share side $EG$. 2. **

1. **State the problem:** We have a point at coordinates $(4, 3)$ on a parallelogram, and we need to translate this point 7 units down on the coordinate plane. 2. **Recall the tran

1. **State the problem:** We need to find how many cylindrical candles the company made given the total volume of wax used, the diameter, and height of each candle. 2. **Formula fo

1. The problem is to understand the equation of a circle and analyze the given circle centered at (4, -7) with radius 5. 2. The general formula for a circle with center $(h, k)$ an

1. **Find the volume of each rectangular prism.** The volume $V$ of a rectangular prism is given by the formula:

1. **Problem statement:** We are given a circle with center P, points W and X on the circle, and a tangent line SU touching the circle at point T. We need to find the measure of an

1. **Problem statement:** We have a right triangle with vertices A, 0, and B. The vertical leg from 0 to A is 33 cm, and the horizontal leg from 0 to B is the radius $r$. We want t

1. **Problem Statement:** We have a secant line intersecting a circle at two points, creating segments outside and inside the circle. The segments outside the circle are labeled 9

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula for a circle's equation:** The standard form is $$ (x - h)^2

1. **State the problem:** We are given a trapezoid with non-parallel sides equal, and two triangles with given side lengths and angles. We need to find the value of $x$. 2. **Analy