📐 geometry

1. **Problem Statement:** We are given a circle with chords AB and CD intersecting at point P inside the circle. We know \(\angle BAP = 40^\circ\) and \(\angle APD = 110^\circ\). W

1. **Problem Statement:** We are given a figure with three intersecting lines forming two adjacent triangles. The angles given are $50^\circ$ (top horizontal angle) and $120^\circ$

1. **Problem Statement:** We are given a geometric diagram with angles $x$, $y$, $50^\circ$, and $120^\circ$. We need to find the values of $x$ and $y$ based on the given angles. 2

1. **Find the value of x in each figure:** (i) Angles on a straight line sum to 180°.

1. **Problem Statement:** Find the area of a sector of a circle with diameter 22 feet and central angle $\frac{3\pi}{4}$ radians. 2. **Formula:** The area $A$ of a sector with radi

1. **Problem Statement:** Prove that the diagonals of a rectangle are equal. 2. **Given:** Rectangle ABCD with diagonals AC and BD intersecting at point O.

1. **Problem statement:** We have a rectangle ABCD formed by two adjacent squares ABFE and CDEF, each with side length 6 cm. Point G is the midpoint of DE, and BG intersects EF at

1. 問題陳述： (1) 三個半徑為2.5 cm的圓形組成的圖形，求其周界。

1. 問題陳述： (1) 計算圖中圓的周界。

1. 問題陳述： 陳先生吃剩的薄餅半徑為 20 cm，求薄餅的周界。

1. **Problem Statement:** We are given several geometric shapes with measurements and need to find missing lengths or areas using the value of $\pi = 3.14$. The shapes include poly

1. **Problem Statement:** We are given two shapes: - A teardrop-shaped figure with a circular top of radius 5 cm and two sides each of length 6 cm.

1. 問題陳述：計算圖形的周界，π取3.14。 2. 公式與規則：

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