📐 geometry

1. **Stating the problem:** We have a square with side length $R=20$ cm. Inside the square, a diagonal arc runs from the upper-left corner to the lower-right corner, and the angle

1. **Problem 6: Find the measure of arc TUV given the circle with tangent point U and angle 108° inside the circle.** 2. The angle formed by two tangents from an external point to

1. **Problem 1: Three externally tangent circles with center distances 7, 8, and 9 inches. Find the area of the largest plate.** 2. The distances between centers of tangent circles

1. **Problem statement:** Given a circle with points P, Q, and T on it, and a tangent at T meeting the line PQ extended at R, prove:

1. The problem asks: What is a helicoid? 2. A helicoid is a type of surface in geometry that can be described as a ruled surface generated by a straight line moving along an axis w

1. **Problem statement:** We have quadrilateral ABCD with given sides and angles: CD = 10 m, DB = 12 m, angle DBA = 90°, angle CDB = 56°, and angle ADB = 34°. We need to find (a) t

1. **Énoncé du problème :** Dans un repère orthonormé direct $(O,\vec{i},\vec{j},\vec{k})$, on considère les points $A(-1,0,1)$, $B(-3,2,2)$, $C(-1,1,2)$ et $D(2,7,-4)$. La droite

1. **Stating the problem:** We have a shape made from 4 identical cubes arranged with three cubes stacked vertically and one cube attached to the middle cube on the right. 2. **Ver

1. **Problem:** Find the area of land, and make a drawing with an example. 2. **Formula for a rectangle:** $$A=l\times w$$

1. **Problem:** Find the area of land, and show a drawing and an example. 2. **Formula for area:** For a rectangle or square, use $$A=l\times w$$.

1. **Find the distance between parks C and D on the map.** Given: Each unit on the grid equals 25 miles.

1. **State the problem:** We are given the volume of a cylinder and asked to find the volume of a rectangular prism with given dimensions. 2. **Recall the formulas:**

1. **State the problem:** Find the surface area of a cylinder with diameter 30 cm and height 40 cm, using $\pi = 3.14$ and no rounding. 2. **Recall formulas:**

1. **Énoncé du problème :** Calculer les longueurs des segments [FD], [AF], [EB], [DK] et la longueur totale du parcours passant par A, F, E, D, K dans la configuration donnée.

1. **Problem Statement:** Calculate the perimeter and area of each composite figure given. ---

1. **Problem Statement:** Calculate the perimeter and area of two composite figures. ---

1. **State the problem:** A 6-m extension ladder leans against a vertical wall with its base 2 m from the wall. We need to find how high up the wall the top of the ladder reaches.

1. **State the problem:** We are given the length of a building on a plan as 22.5 cm and the actual length of the building as 29.25 m. We need to find the scale of the plan as a si

1. **State the problem:** We have an isosceles triangle ABC with an angle of 130° at vertex B. We need to determine which statement about the angles is true. 2. **Recall properties

1. **State the problem:** We have an isosceles triangle ABC with an angle of 130° at vertex B. We need to determine which statement about the angles is true. 2. **Recall properties

1. **Problem:** Find the perimeter and area of the right triangle with legs 8.2 cm and 10.5 cm. 2. **Formula:**