📐 geometry

1. The problem is to construct a rectangle that can be divided into four identical squares. 2. To solve this, we need to understand that four identical squares arranged together fo

1. **Problem statement:** Construct a rectangle that can be divided into four identical squares. 2. **Understanding the problem:** A rectangle divided into four identical squares m

1. Vấn đề: Chứng minh góc $\angle FDO = 90^\circ$. 2. Công thức và quy tắc: Để chứng minh góc vuông, ta cần chứng minh rằng hai đoạn thẳng tạo thành góc đó vuông góc, tức là tích v

1. **Đề bài:** Cho đường tròn $(O)$ và điểm $A$ nằm ngoài đường tròn. Từ $A$ vẽ hai tiếp tuyến $AB$, $AC$ với tiếp điểm $B$, $C$. Vẽ đường kính $BD$ của đường tròn $(O)$; $AD$ cắt

1. **Problem statement:** Find the lengths of $DC$ and $BD$ in the given figure where $BD$ is perpendicular to $BA$ and $DC$ is parallel to $BA$. 2. **Given:**

1. **Problem Statement:** Find the area of a triangle with base $b$ and height $h$. 2. **Formula:** The area $A$ of a triangle is given by the formula:

1. مسئله: رسم محور x و y در دستگاه مختصات دکارتی. 2. محور x (محور افقی) خطی است که از چپ به راست کشیده شده و مقدار y در آن صفر است.

1. **Problem Statement:** A rectangular pond has a length of 75 metres and a breadth of 50 metres. A uniform bank of width 4 metres is built all around the outside of the pond. Ins

1. The problem is to find the sum of two angles: 45 degrees and 60 degrees. 2. The formula for the sum of angles is simply addition: $$\text{Sum} = \theta_1 + \theta_2$$

1. সমস্যাটি হলো একটি বৃত্তের সমীকরণ $b(x,y) = x^2 + y^2 = 4$ এবং একটি বিন্দু $(4,3)$ এর অবস্থান নির্ণয় করা। 2. বৃত্তের সমীকরণ $x^2 + y^2 = r^2$ যেখানে $r$ হলো বৃত্তের ব্যাসার্ধ। এ

1. **Énoncé du problème :** Vérifier la véracité des affirmations vectorielles données et écrire leurs réciproques en précisant si elles sont vraies ou fausses.

1. **State the problem:** We have a triangle with angles labeled as follows: the top vertex angle is 80 degrees, the left base angle is $2x - 6$, and the right base angle is $3x +

1. **Stating the problem:** We need to find the surface area of a rectangular prism (cuboid) with length $24$ cm, width $12$ cm, and height $18$ cm.

1. **State the problem:** We are given a triangle LMN with area 133 cm², side LM = 16 cm, and side MN = 21 cm. We need to find the angles \(\angle LMN\) and \(\angle MNL\). 2. **Re

1. Énonçons le problème : recalculer la distance indiquée en jaune. 2. La distance entre deux points dans un plan peut être calculée avec la formule de la distance :

1. Énonçons le problème : Calculer la distance en jaune associée à un angle de 30° dans un cercle ou une configuration géométrique donnée. 2. Formule utilisée : Pour une distance l

1. **Problem statement:** Calculate the area of the shaded portion of the triangle with two equal sides of length 8 cm and an included angle of 54°. 2. **Formula used:** The area $

1. **Problem:** Find the value of the angle given choices 150°, 120°, 75°, 60°. Since no specific question is stated, we move to the next problem.

1. **Stating the problem:** We have triangle ABC with an exterior angle bisector AD' at vertex A. We are given that segment D'C is longer than AC and segment D'B is longer than AB.

1. **Problem statement:** We have a quadrilateral with equal diagonals. The segments joining the midpoints of opposite sides have lengths 13 and 7. We need to find the area of this

1. **Problem Statement:** We need to find the fraction of the whole large square that is shaded in part (a). 2. **Understanding the figure:** The large square is divided into 4 equ