📐 geometry

1. **Stating the problem:** We are given the system of equations involving direction cosines $a,b,c$ and $f,g,h$:

1. **Exercice 02**: Soit $ABC$ un triangle rectangle en $A$. 1. Construire $C'$, le symétrique de $C$ par rapport à $A$ signifie que $A$ est le milieu de $[CC']$. Formellement, si

1. **State the problem:** We have a triangle with vertices Q(-9, -7), R(-9, -2), and S(-4, -4). We want to find the coordinates of the vertices after reflecting the triangle over t

1. **State the problem:** We have points A, B, C, D on a circle and two triangles ADE and ABF formed with points E and F outside the circle. Given angles:

1. The problem is to find the circumference of a circle given its radius. 2. The formula for the circumference $C$ of a circle with radius $r$ is:

1. The problem is to find the area of a square. 2. The formula for the area of a square is given by:

1. **State the problem:** Balena has a circular garden with radius 10 m and wants to cover it completely with grass seed. Each box covers 46 m². We need to estimate how many boxes

1. **Problem statement:** We have an isosceles triangle with a base of length $2$ cm and a perimeter of $10$ cm. We need to find the length of the two equal sides. 2. **Formula and

1. **Problem statement:** We have a hollow shape made from four right-angled triangular tiles and four square tiles. Each triangular tile has sides 3 cm and 4 cm, and the shape is

1. **Problem Statement:** Construct a line segment AB of length 7.5 cm, its perpendicular bisector, a semicircle with AB as diameter, and perform several geometric constructions in

1. **Problem Statement:** We have several problems involving volumes and areas of prisms, cylinders, and tanks.

1. **Problem statement:** We need to find the area of the shaded minor segment in a quadrant of a circle with radius 6 cm. 2. **Understanding the problem:** A quadrant is one-fourt

1. **Problem statement:** We have a circle with radius $r=3$ cm and a minor sector with central angle $\theta=135^\circ$. We need to find the area of the minor segment and the peri

1. **Problem statement:** We have an equilateral triangle ABC with side length 10 cm. A circle centered at point A intersects the midpoints of sides AB and AC. We need to find the

1. **Problem statement:** We have a fan with radius $30$ cm and $4$ blades, each blade subtending a central angle of $30^\circ$. We need to find the total area covered by the $4$ b

1. **State the problem:** We have a circular cake with radius $r=10$ cm. We want to cut it into identical sector pieces, each with a perimeter of approximately 23.93 cm.

1. Énoncé du problème : ABCD est un parallélogramme avec les longueurs suivantes : $DA=6$, $DB=9$, $DE=2$, et $AB=8$. 2. Rappel : Dans un parallélogramme, les côtés opposés sont ég

1. **Problem statement:** We need to find the volume of the triangular prism given angle $\angle BDE = 25^\circ$, length $BD = 63$ m, and base length $AD = 21$ m. 2. **Understandin

1. **Problem Statement:** We need to find ten times the perimeter of the shaded semicircle with diameter 10 cm. 2. **Formula for the perimeter of a semicircle:** The perimeter $P$

1. **Problem statement:** Prove that triangle OAS is isosceles with principal vertex A.

1. **Problem Statement:** We have an isosceles triangle inscribed in a circle with two equal sides meeting at the top vertex called the "centre." The angles at the base are labeled