📐 geometry

1. **Problem Statement:** Find the circumference of the circle with diameter 4 cm using $\pi = 3.14$. 2. **Formula:** The circumference $C$ of a circle is given by

1. **Problem Statement:** Find the circumference of each circle using the given values and the specified value of $\pi$. 2. **Formula:** The circumference $C$ of a circle is given

1. **State the problem:** We need to find the values of angles $x_1$ and $x_2$ in a geometric figure involving a circle and a triangle with given angles $130^\circ$, $80^\circ$, an

1. **Stating the problem:** We are given a circle with points B, C, and E on the circumference, and a triangle ADE outside the circle with angles 25° and 50° at point A. We need to

1. **Problem statement:** We have a circle with center O and points A, B, C on the circumference. CD is a tangent at C. Given \(\angle BCD = 40^\circ\) and \(\angle OAB = 3 \times

1. **Problem 1: Rectangle ABCD with diagonal AC and triangle ADE inside** - Given: ABCD is a rectangle, so all angles are 90°.

1. The problem involves finding the value of angle $x$ in two different triangles based on the given angles. 2. In the first triangle ABC, we know angle $B = 51^\circ$ and angle $A

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