📐 geometry

1. **Problem statement:** Given the diagram with points F, E, D, A, B, C and angles \(\angle CED = 24^\circ\) and \(\angle BAE = 60^\circ\). Lines EA and EC bisect \(\angle FEB\) a

1. Let's start by stating the problem: We want to solve a geometry problem, but since the exact problem isn't specified, let's consider a common geometry problem such as finding th

1. **Stating the problem:** You asked why we assume that the lines EA and EC bisect the angles, and whether only perpendicular bisectors divide angles into two equal parts.

1. **Stating the problem:** We are given a geometric figure with points F, E, D, A, B, and C.

1. بين أن المستقيمين (HK) و (LN) متوازيان. - إذا كان OH عمودياً على HK و OH = 3.6 cm، و HK = 3 cm، و KN = 5.4 cm، و KH = 2 cm، فإن الزوايا المتقابلة متساوية مما يدل على توازي (HK)

1. نبدأ ببيان المسألة: لدينا مثلث قائم الزاوية في K، حيث طول الوتر IJ = 13 سم، والزاوية x عند النقطة J تساوي 25°. 2. نستخدم قانون جيب التمام أو قوانين المثلثات القائمة لحساب طول ال

1. **State the problem:** We need to find the area of a segment of a circle with radius $12$ cm and a central angle of $60^\degree$. 2. **Formula and explanation:** The area of a s

1. **Problem:** Construct a rectangle in which one of the diagonals divides the angles into 30° and 60°. 2. **Understanding the problem:** In a rectangle, all angles are 90°. The d

1. **State the problem:** Find the perimeter of a square with side length 3.5 cm. 2. **Formula:** The perimeter $P$ of a square is given by

1. **State the problem:** Find the area of a triangle with base 12 cm and height 9 cm. 2. **Formula:** The area $A$ of a triangle is given by the formula:

1. The problem is to find the area of a parallelogram given its base and height. 2. The formula for the area of a parallelogram is $$\text{Area} = \text{base} \times \text{height}$

1. **Stating the problem:** We are given the cosine rules for angles in a triangle: $$\cos A=\frac{b^2+c^2-a^2}{2bc}$$

1. **Problem statement:** We have a right triangle ABC with a right angle at B. The side AB is 12 cm, and the hypotenuse AC is 13 cm. We need to find the length of side BC. 2. **Fo

1. **Problem Statement:** Find the height and diameter of an oblique circular cylinder given the axis length and the angle with the base plane.

1. **Nêu bài toán:** Cho tam giác đều ABC có cạnh bằng 3. Điểm M thỏa mãn: $$2MA^2 + MB^2 + MD^2 = 18$$. Tìm bán kính đường tròn mà tập hợp điểm M thuộc về. 2. **Công thức và kiến

1. **Problem Statement:** Label an oblique circular cylinder with a 45 degrees angle with the plane of its base.

1. **Stating the problem:** We have a half-cylinder shape with a bottom diameter of 64 cm, a top diameter of 110 cm, and a total length of 455 cm. It is cut into 4 equal pieces alo

1. **Stating the problem:** We have three angles related by the diagram: one angle is $5y$, another is $4y$, and the angle between these two rays is $y$. We want to find the value

1. **Problem statement:** Find the coordinates of the point that divides the points $P(8,9)$ and $Q(-7,4)$ internally in the ratio $2:3$ and externally in the ratio $4:3$. 2. **For

1. Vous avez demandé de reproduire une figure, mais aucun détail ou description de la figure n'a été fourni. 2. Pour pouvoir vous aider, j'ai besoin d'une description précise ou d'

1. **Énoncé du problème :** Vérifier que $\overrightarrow{A J} = 3 \overrightarrow{A C}$ sachant que $\overrightarrow{J C} = \frac{2}{3} \overrightarrow{J A}$.