📐 geometry

1. The problem asks for the equation for the diameter of a circle. 2. Recall that the diameter of a circle is the length of a straight line passing through the center of the circle

1. **Stating the problem:** We need to match the sides of a right-angled triangle relative to the angle $\theta$. The triangle has a right angle, and $\theta$ is one of the other a

1. The problem asks to match the sides of a right triangle relative to the angle $\theta$. 2. In a right triangle, the hypotenuse is always the longest side opposite the right angl

1. **Énoncé du problème e)** Déterminer la perpendiculaire commune entre la diagonale $BD'$ et la diagonale de face $A'C'$ dans un cube d'arête $a$, puis calculer la distance entre

1. **State the problem:** We need to complete the table using the formula for arc length $$s = r\theta$$ where $$r$$ is the radius, $$\theta$$ is the angle in radians, and $$s$$ is

1. **State the problem:** Find the area of a square with side length 5. 2. **Formula:** The area $A$ of a square with side length $s$ is given by:

1. **State the problem:** We need to find the arc length $s$ using the formula $s = r\theta$, where $r$ is the radius and $\theta$ is the angle in radians. 2. **Convert the angle f

1. **Problem Statement:** Find the value of $x$ given two polygons with sides labeled $x+5$, 4 and 5, 15 respectively, assuming the polygons are similar and corresponding sides are

1. **State the problem:** We need to complete the table using the formula for arc length $$s = r\theta$$ where $$r$$ is the radius and $$\theta$$ is the angle in radians. We will c

1. **State the problem:** We need to find the number of radians in a central angle whose arc length is 23 of a circle, expressed in terms of $\pi$ radians and rounded to three sign

1. **State the problem:** Calculate the area of the house, the driveway, and the yard given the total property area and dimensions. 2. **Given:**

1. **Problem Statement:** We have a trapezoid with two vertical sides labeled $y$ inches and $x$ inches, and a horizontal base of 14 inches. The trapezoid has a right angle at the

1. The problem states that point N is the incenter of triangle ABC, and we are given expressions for segments ND and NE. We need to find NF. 2. Since N is the incenter, it is equid

1. **Problem statement:** Given a quadrilateral WXYZ with diagonals WX and WR, and the lengths XZ = 46 and WR = 21, find the length WX. 2. **Understanding the problem:** We are giv

1. **Problem Statement:** Find the area of the irregular shape with a rectangular cut-out on the top-left side, given side lengths labeled as $x+5$, $3$, $x-2$, and $x$. 2. **Under

1. **Problem statement:** Triangle C is rotated 180° clockwise about the origin. We need to find the new location of Triangle C after this rotation. 2. **Rotation formula:** For a

1. **State the problem:** We have two similar triangles, $\triangle ABC \sim \triangle ADE$, and we need to find the length $u = AE$. 2. **Recall the property of similar triangles:

1. **State the problem:** We are given a triangle with an internal point E on side BC. We know one angle is $46^\circ$ at vertex C and another angle $y^\circ$ at vertex B between s

1. **Problem statement:** Given parallelogram KLMN with side KL labeled as $x$, side LM as 16, and other segments marked with equal lengths, find the value of $x$. 2. **Recall prop

1. **State the problem:** We have triangle $\triangle STU$ with side $s = 250$ inches opposite angle $S$, angle $\angle U = 17^\circ$, and angle $\angle S = 52^\circ$. We need to f

1. **State the problem:** We have triangle UVW with side $w=35$ inches opposite angle $W=154^\circ$, and angle $U=10^\circ$. We need to find the length of side $u$ opposite angle $