📐 geometry

1. The problem asks to create two squares each with side length 10 cm, divided into 100 equal smaller squares. 2. Each small square will have side length $\frac{10}{10} = 1$ cm bec

1. **Stating the problem:** We have a quadrilateral ABDM with diagonal AC. Angles at vertices are labeled as follows: angles $p$ and $w$ at vertex A, angle $t$ at vertex B, and ang

1. **Stating the problem:** Triangles $XYZ$ and $PQR$ are similar. Given sides $XY=35$, $YZ=30$, $XZ=X$, and corresponding sides $PQ=28$, $QR=12$, $PR=n$, find $X$ and $n$. 2. **Fo

1. The problem asks to find the values of $x$, $y$, and $z$ given some angles: $40^\circ$, $121^\circ$, and others labeled $A$, $B$, $C$, $D$, $z^\circ$, $x^\circ$, $y^\circ$. 2. S

1. **Stating the problem:** We need to find the values of angles $x$, $y$, and $z$ given some angles and possibly relationships between them. 2. **Analyzing the given information:*

1. **State the problem:** Find the length of the longest segment that can fit into a cube with side length 4 cm. 2. **Formula used:** The longest segment inside a cube is its space

1. **State the problem:** We have a quadrilateral ABCD with diagonals intersecting inside, and various angles given including two angles labeled $x$ at vertices A and D. We need to

1. **State the problem:** In rectangle ABCD, we are given that DE = 3x + 6 and BE = 5x - 6. We need to find the value of $x$. 2. **Understand the properties of a rectangle:** In a

1. **State the problem:** We are given a quadrilateral ABCD with interior angles \(\angle A = 50^\circ\), \(\angle B = 60^\circ\), \(\angle C = 10^\circ\), and \(\angle D = 70^\cir

1. **Problem statement:** Find the area of the corridor outside the square classroom ABCD, express it in terms of $x$, then find $x$ and the area of the classroom given the corrido

1. Problem: Calculate the area of a triangle with base $b=10$ units and height $h=6$ units. 2. Formula: The area $A$ of a triangle is given by $$A=\frac{1}{2} \times b \times h$$

1. **State the problem:** We need to find the image of triangle \(\triangle XYZ\) with vertices \(X(8,4)\), \(Y(4,6)\), and \(Z(8,14)\) after two transformations: reflection across

1. The problem asks for the size of the reflex angle given a smaller angle of approximately 45 degrees. 2. Recall that a reflex angle is the larger angle formed by two rays, greate

1. **State the problem:** We have a circle given by the equation $$x^2 + y^2 + x - 15 = 0$$ and one end of its diameter is at the point $(2, -3)$. We need to find the coordinates o

1. **State the problem:** We need to find the equation of a circle that passes through the points $(0,0)$ and $(4,2)$, and whose center lies on the line $x + y = 1$. 2. **Formula f

1. **Problem Statement:** Find the equation of a circle that touches the coordinate axes at points $(a,0)$ and $(0,a)$. 2. **Understanding the problem:** A circle touching the coor

1. Bài toán yêu cầu so sánh các góc của tam giác ABC dựa trên độ dài các cạnh cho trước. 2. Quy tắc quan trọng: Trong tam giác, góc đối diện với cạnh dài hơn sẽ lớn hơn.

1. **State the problem:** Find the equation of a circle that touches the coordinate axes at points (1,0) and (0,1). 2. **Understand the problem:** A circle touching the coordinate

1. **State the problem:** Find the equation of a circle that touches the x-axis at the point $(3,0)$ and passes through the point $(1,2)$. 2. **Understand the problem:** A circle t

1. The problem is to understand how to determine that the third angle in a triangle is 30 degrees. 2. The key rule is that the sum of the interior angles in any triangle is always

1. **Stating the problem:** We have a circle with center O and points P, Q, R, S on the circumference forming quadrilateral PQRS. Outside the circle, triangle PST is connected with