📐 geometry

1. The problem presents a set of 12 different geometric figures described by vertices' labels and numbers at corners or edges. 2. The figures include triangles with numbers at vert

1. **State the problem:** Given a circle with center O and points P, Q, R, S, T on its circumference, with line TOQ straight and T on PS, and PQ = QR, find: - (8.2.1) angle $\hat{P

1. **State the problem:** We have a ray of light passing through point $P(2, 3)$, reflecting on the x-axis at point $A$, and the reflected ray passes through point $Q(5, 4)$. Point

1. Stating the problem: We need to find the volume of a pentagonal pyramid given the base length $b = 11$ cm, apothem $a = 7.57$ cm, and height $h = 16$ m. 2. Convert height to cm

1. **State the problem:** We have a 50-dimensional hypercube with side length 1. The boundary is defined by points where at least one coordinate $x_j$ lies in either $[0,0.05]$ or

1. **State the problem:** We have a $50$-dimensional hypercube with side length $1$. The boundary is defined as points where at least one coordinate $x_j$ is in $[0,0.05]$ or $[0.9

1. **Énoncé du problème** : Dans un repère orthonormé (O; I; J), on étudie les points A(2, -3), B(-2, -1) et C(4, 1). 1.a) Placer les points A, B et C dans le plan.

1. The problem states that a circle has a diameter of 8 units. We need to find the circumference of the circle. 2. Recall the formula for the circumference $C$ of a circle in terms

1. The problem is to find the area of a triangle. 2. The area $A$ of a triangle with base $b$ and height $h$ is given by the formula:

1. **Énoncé du problème :** Nous avons un plan muni d'un repère orthonormé (oi, j, k). On considère les points $A(4 ; -2)$, $B(-3 ; 2)$, $C(3 ; 6)$ dans ce plan. 2. **Placement des

1. We are given that angle A measures 135° in the figure and we want to find the measure of angle B. 2. Assuming angles A and B are related and the problem suggests understanding t

1. The problem states that the volume of a cone is 565.7 and the height is 15 cm. We need to find the radius and the surface area of the cone. 2. The volume $V$ of a cone is given

1. **Énoncé du problème :** Nous avons un triangle ABC rectangle en A avec BC = 2AC.

1. \textbf{הבעיה:} \text{נתון טרפז שווה שוקיים } ABCD \text{ עם } AB \parallel DC.\ נקודה } O \text{ היא אמצע האלכסון } BD.\

1. **State the problem:** We have a triangle ABC with angles $A=47^\circ$, $C=66^\circ$, and the perimeter is 75 cm. We need to find side $b$ to the nearest tenth. 2. **Find angle

1. Let's first understand the original problem, which involves solving using triangle MKG. 2. The question asks if there is an alternative method without constructing triangle MKG.

1. The question asks about constructing segment $MK$ to form another triangle in the given figure. 2. To construct segment $MK$ to create a new triangle, we need to identify points

1. **State the problem:** Prove that in the cyclic quadrilateral EFGH with chords EH and FG produced to meet at K, and M on EF such that MG is parallel to EK and KG equals EF, the

1. Problem Statement: Given a triangle SLM with sides SL=13m, LM divided into segments 2m and 5m, and SM labeled as $k$, find the length of $k$ using the given information and rela

1. Problem: We are given a quadrilateral ABCD with sides AB = 11 cm, BC = 4 cm, AC = 13 cm, CD = 8 cm, and angle \(\angle ADC = 80^\circ\). We need to find the size of the angle \(

1. You asked to show the shaded region, but no specific function or inequalities were provided. 2. To find and show a shaded region, I need an inequality or a system of inequalitie