📐 geometry

1. Problem 1 asks to find the measure of arc AN. Given angles inside circle R are 100°, 65°, and 30°. AE is a diameter.

1. **Stating the problem:** We have three 3D geometric shapes around a clock tower: a rectangular prism with dimensions 38 cm height and 15 cm width (depth unspecified), a triangul

1. The problem asks us to find the volume and surface area of a pyramid based on a given picture, and verify if your answer is correct. 2. To find the volume $V$ of a pyramid, use

1. **Stating the problem:** Calculate the volume and surface area of a triangular pyramid with base edges 18 cm and side edges 21 cm and 18.5 cm. 2. **Volume calculation:** The vol

1. Let's analyze the left diagram first. According to the intersecting chords and secants properties in a circle: For a point outside the circle where a secant intersects the circl

1. **State the problem:** We need to find the volume and surface area of the triangular pyramid with edges 21 cm, 18.5 cm, and base side 18 cm.

1. Problem: Write the equation to solve for $x$ in each circle geometry figure using the intersecting chords and secant-tangent theorems. 2. a. Two chords intersecting inside the c

1. Problem: Find the equations relating the segments in each circle figure to solve for $x$ using chord and secant-tangent theorems. 2. For each part:

1. The problem asks to find or explain the meaning of the angle $WXV$ in a geometric context. 2. Typically, $WXV$ denotes the angle formed at point $X$ by the points $W$ and $V$.

1. **State the problem:** We are given a rhombus WXYZ with given angles: angle XYZ = 65°,

1. **State the problem:** We need to find the area of the compound figure described. 2. **Analyze the shape:** The shape is a large rectangle with a smaller rectangular notch remov

1. The problem is to find the distance between two points using the distance formula. 2. The distance formula between points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $$d=\sqrt{(x_2-x_1)^2+

1. The problem asks to find the value of $h$ for point $Q(h, 5)$, given points $P(-7, -3)$ and $R(8, 9)$ forming a right triangle with $Q$ on the hypotenuse. 2. Since $Q$ lies on t

1. Stating the problem: We need to find the value of $h$ for the right triangle with vertices $P(-7,-3)$, $Q(h,5)$, and $R(8,9)$, where the right angle is at point $P$. 2. Since th

**Exercice 3 :** 1. Soit ABC un triangle, E est point tel que $\overrightarrow{AE} = \frac{1}{2} \overrightarrow{AB}$, donc E est le milieu du segment [AB].

1. The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves using ordered pairs $(x,y)$. 2. It consists of two perpendicular number lines: t

1. **Énoncé du problème :** On a les mesures orientées suivantes entre vecteurs :

1. **State the problem:** We have trapezium ABCD with AD parallel to BC.

1. **Identify which figure represents an angle.** - (a) → is a ray, not an angle.

1. Le problème demande de déterminer plusieurs mesures principales d'angles orientés entre différents vecteurs donnés. Données :

1. **Problem statement:** We have two circles with centers A and B each of radius 10 cm. B lies on circle A, so AB = 10 cm. Points C and D are intersections of the circles. E is on