📐 geometry

1. **Problem statement:** We have two equal circles with centers $O$ and $O'$ touching at $X$. The line $OO'$ is extended to meet the circle centered at $O'$ at $A$. The line $AC$

1. **Problem statement:** Given angle $FGC = 98^\circ$ and arc $FC = 60^\circ$, find the measure of arc $FB$. 2. **Understanding the problem:** In a circle, the measure of an inscr

1. **State the problem:** We need to find the size of angle $x$ in a figure where a large triangle is intersected by two parallel lines creating a smaller triangle inside it. Given

1. Let's clarify the problem: You mentioned the adjacent side isn't the same for the white triangle. This suggests we are dealing with a right triangle and need to identify the cor

1. **State the problem:** Given rhombus ABCD with AE \cong BE, prove ABCD is a square. 2. **Given:** ABCD is a rhombus and AE \cong BE.

1. **State the problem:** We have a cuboid container with dimensions 10 cm (height), 5 cm (width), and 4 cm (depth). The volume of water inside is 120 ml, which equals 120 cm³. 2.

1. **State the problem:** We need to find the volume of a shape formed by a large cuboid with a smaller cuboid removed from one corner. 2. **Identify dimensions:**

1. **State the problem:** We need to find the volume of a shape formed by a large cuboid with a smaller cuboid removed from one of its corners. 2. **Formula for volume of a cuboid:

1. **Problem statement:** We are given the perimeter of a quarter circle as 164.22 millimeters and need to find the radius $r$ of the quarter circle, rounded to the nearest hundred

1. **הבעיה:** במשולש ABC חסום במעגל שמרכזו O כך ש־AB הוא קוטר המעגל. הנקודה E נמצאת על הצלע BC, והנקודה F נמצאת על הקטע BO.

1. **State the problem:** We are given a trapezoid with an area of 33 square miles, top base length 8 miles, bottom base length 3 miles, and one leg length 8 miles. We need to find

1. **State the problem:** We have a trapezoid with bases of lengths 5 (longer base) and 2 (shorter base), and height 1. There is a dotted line inside the trapezoid parallel to the

1. **State the problem:** We are given a trapezoid with an area of 42 square kilometers. The trapezoid has bases of lengths 4 km and 8 km, and we need to find its height $h$. 2. **

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 18 inches and 7 inches, and a height of 20 inches. 2. **Formula for the area of a trapezoid:

1. **State the problem:** We need to find the area of a trapezoid with top base $0.3$ miles, bottom base $0.8$ miles, and height $0.6$ miles. 2. **Formula for the area of a trapezo

1. **State the problem:** We need to find the area of a trapezoid with the following dimensions: top base $=5$ m, bottom base $=11$ m, and height $=4$ m. 2. **Formula for the area

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 12 km and 4 km, and a height of 3 km. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We need to find the area of a trapezoid with top base $6$ mm, bottom base $8$ mm, and height $4$ mm. 2. **Formula for the area of a trapezoid:**

1. **Problem Statement:** Calculate the angle that line segment $AJ$ makes with the base $ABHG$ of the prism, given the dimensions and angles of the pentagonal prism. 2. **Understa

1. The problem asks: If you look at the 3D stepped pyramid of cubes from the front, what 2D shape will you see? 2. The 3D object is a stepped pyramid with 3 levels, where each leve

1. **Problem Statement:** You are asked to determine what the front view of a 3D isometric stacked block structure looks like.