📐 geometry

1. সমস্যাটি হলো: সমকোণী ত্রিভুজ ABC তে, যেখানে \(\angle B = 90^\circ\) এবং বাহু AC = 10 সেমি। ত্রিভুজটির বাহুগুলির দৈর্ঘ্যের বর্গের সমষ্টি কত? 2. সূত্র: সমকোণী ত্রিভুজের ক্ষেত্রে,

1. **Nêu bài toán:** Từ điểm $M$ nằm ngoài đường tròn $(O,R)$ sao cho $OM=2R$. Vẽ hai tiếp tuyến $MA$, $MB$ với đường tròn $(O)$, $A$, $B$ là hai tiếp điểm. Gọi $H$ là giao điểm củ

1. مسئله: مجموع زوایای داخلی یک چندضلعی منتظم با 15 ضلع را پیدا کنید. 2. فرمول مجموع زوایای داخلی هر چندضلعی با $n$ ضلع به صورت $$180(n-2)$$ درجه است.

1. The problem is to find the value of angle $x$ in a triangle where the other two angles are $115^\circ$ and $35^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the i

1. The problem is to create assertion-reason type questions for the chapter "Construction of Triangles" for class VIII. 2. Assertion-Reason questions consist of two statements: an

1. **State the problem:** Find the equations of the altitudes of the triangle with vertices A(0,4), B(4,6), and C(-2,-2). 2. **Recall the definition:** An altitude of a triangle is

1. **Problem statement:** In triangle ABC, given $\angle A = 40^\circ$, $\angle B = 80^\circ$, and side $b = 14.4$ feet, find $\angle C$ and side $c$. 2. **Step 1: Find $\angle C$*

1. مسئله: ما می‌دانیم که EB و BC و ABCD مربع هستند و مساحت EB برابر مساحت ABCD است. باید مساحت مثلث ABE را محاسبه کنیم.

1. The problem involves understanding the arrangement of eight circular logos in a grid of two rows and four columns, each representing a FIFA tournament. 2. The logos are arranged

1. **مشكلة:** لدينا دائرة نصف قطرها $3$ وحدات، ونريد حساب مساحة الجزء المظلل الذي يمثل قطاع دائري بزاوية $60^\circ$. 2. **الصيغة المستخدمة:** مساحة القطاع الدائري تُحسب بالعلاقة:

1. **Problem statement:** Given a rhombus ABCD with |AC| = |DC|, angles m(ABC) = 70°, m(ACB) = 40°, and m(BDC) = 75°, find the measure of angle m(BCD) = \(\alpha\). 2. **Recall pro

1. \textbf{Đề bài:} Cho tam giác ABC vuông tại A với AB<AC, AM là trung tuyến. Kẻ ME vuông góc với AB tại E, MF vuông góc với AC tại F. AM cắt EF tại G, CG cắt AB tại R. Chứng minh

1. **Énoncé du problème :** Nous avons un cercle de centre $O$ avec des points $A$, $B$, et $M$ sur le cercle.

1. **Nêu bài toán:** Cho nửa đường tròn tâm $O$ bán kính $R$ với đường kính $AB$. Hai tiếp tuyến $AX$ và $BY$ được vẽ tại $A$ và $B$. Trên nửa đường tròn lấy điểm $C$ sao cho $AC <

1. The problem asks to describe the transformations that map a frieze pattern onto itself. 2. Frieze patterns are infinite strips with repeating motifs. The transformations that ma

1. **Problem statement:** Given that $m(\angle DAB) = m(\angle C)$ in the figure, find the value of $x$. 2. **Understanding the problem:** The equality of angles $m(\angle DAB) = m

1. **Stating the problem:** We have two rectangular prisms side by side with given surface areas and volumes, and we need to find the unknown lengths. 2. **Given data:**

1. **State the problem:** We need to find the projection of the shortest side of a triangle with sides 6, 7, and 8 onto the longest side. 2. **Identify the sides:** The shortest si

1. **بيان المسألة:** لدينا مثلث قائم الزاوية بزاوية قائمة عند النقطة ب، طول القاعدة ٤ سم، والارتفاع ٣ سم. هناك قطاع دائري مركزه عند النقطة ١ بزاوية ه°، وطول القوس ٢ سم على الوتر ١

1. **State the problem:** Find the equations of the altitudes of the triangle with vertices A(0,4), B(4,6), and C(-2,-2). 2. **Recall the definition:** An altitude of a triangle is

1. The problem is about proving that all angles formed by bisectors of angles are equal. 2. When an angle is bisected, it is divided into two equal parts. This means each formed an