📐 geometry

1. The problem is to find the coordinates of point A without using the BD equation. 2. To solve this, we need to understand what information is given about point A and the context

1. Problem: Find the ratio of areas of two squares with given side lengths. 2. Formula: The ratio of areas of two squares is the square of the ratio of their corresponding side len

1. **Problem Statement:** Given triangle ABC with vertices B(5,0), C(1,4), and A unknown. D is the midpoint of AC and lies on the y-axis. AE is the perpendicular bisector of BC and

1. Bài toán yêu cầu giải quyết mà không sử dụng tọa độ và vector. 2. Để giải các bài toán hình học phẳng mà không dùng tọa độ và vector, ta thường sử dụng các định lý hình học cổ đ

1. \textbf{Đề bài:} Cho hình vuông ABCD, trên cạnh BC lấy điểm M, AM cắt đường thẳng CD tại điểm N. Kéo dài DM cắt BN tại I. Chứng minh rằng CI vuông góc với AN. 2. \textbf{Phân tí

1. The problem describes a triangular region bounded by three lines: $x=1$, $y=2$, and $x+y=10$. 2. To understand the shape and find the vertices of the triangle, we find the inter

1. **Problem:** Find the largest volume of a cube that can be enclosed in a sphere of diameter 2 cm. 2. **Understanding the problem:** The cube is inscribed inside the sphere, so t

1. **Problem statement:** We have two identical rectangular prisms, each with height $90$ cm and a square base with side length $s$ cm. Each prism has surface area $K$ cm$^2$. When

1. **Problem:** Find the side length of a rhombus given its diagonals are 30 cm and 16 cm. 2. **Formula:** The diagonals of a rhombus bisect each other at right angles. Each side $

1. مسئله: محیط ذوزنقه متساوی الساقین ABCD را با داده‌های $BK=4$، $DC=11$ و $AB=5$ بیابید. 2. فرمول محیط ذوزنقه: محیط برابر است با مجموع طول چهار ضلع:

1. **Énoncé du problème** : Soit $M$ un point du cercle circonscrit $\mathscr{C}$ au triangle équilatéral $ABC$ de côté 2, distinct de $\Omega$ et $A$. On pose $M_1 = S(M)$ et $M_2

1. נניח כי במשולש ABC, AB \perp BC, ו- BD הוא הגובה ליתר AC. 2. נתון כי BE הוא תיכון ליתר AC, כלומר E הוא נקודת האמצע של AC.

1. **Problem statement:** Given triangle ABC with points D and E such that BD \perp CE and DC = BE = \frac{1}{2} BC, prove that triangle ABC is equilateral. 2. **Known facts and fo

1. **Problem 1: Find the centre of enlargement and image of Q(1,1)** under enlargement with scale factor $-3$ that maps $P(3,6)$ to $P_1(7,18)$. 2. The formula for enlargement with

1. **Problem Statement:** Given point $A(-1,-5)$ and its reflection image $A'(3,-3)$, find the equation of the mirror line in the form $ax + by + c = 0$. 2. **Reflection Properties

1. **Problem Statement:** Given point $A(-1,-5)$ and its reflection image $A'(3,-3)$, find the equation of the mirror line in the form $ax + by + c = 0$. 2. **Reflection Property:*

1. **State the problem:** Find the area of the polygon formed by the points $(-5,-4)$, $(2,-2)$, and $(1,3)$. Since there are three points, the polygon is a triangle. 2. **Formula

1. The problem states that the part labeled A is a triangle. We need to analyze or solve something related to this triangle. 2. To work with triangles, common formulas include the

1. **State the problem:** We need to find the area of the polygon divided into three sections A, B, and C with given dimensions: total height 7 m, right segment height 2 m, vertica

1. **Problem:** Determine if the given pairs of triangles are similar, write the similarity statement, and name the theorem used. 2. **Key Theorems for Triangle Similarity:**

1. សូមបញ្ជាក់បញ្ហា៖ អ្នកចង់ដឹងពីរបៀបគណនាអំពីសំណុំរូបត្រីកោណ (Group 1)។