📐 geometry

1. **Problem statement:** We have a circle with center $O$ and radius $10$ cm. Two chords $AB$ and $PQ$ are parallel, with lengths $AB=12$ cm and $PQ=16$ cm. The line $OX$ is perpe

1. Given two triangles ABC and PQR, we are asked to find the condition for them to be congruent under the given angle equalities. 2. The problem states:

1. பிரச்சினையை விளக்குக: வட்டத்தில் AB விட்டமாகும், AC=8 மற்றும் BC=6 என கொடுக்கப்பட்டுள்ளது. வட்டத்தின் ஆரை (radius) காண வேண்டும். 2. முக்கிய விதி: வட்டத்தில் AB விட்டம் என்பது வட

1. பிரச்சினையை விளக்குக: வட்டத்தின் மையம் O ஆகும். கோணமான ∠OBA = 50° என கொடுக்கப்பட்டுள்ளது. நமக்கு x என்ற கோணத்தின் மதிப்பை காண வேண்டும். 2. வட்டத்தில், மையம் O மற்றும் வட்டத்தின்

1. பிரச்சினையை விளக்குதல்: PQRS என்ற நாற்பக்கத்தில், SR, T வரிகள் மற்றும் PT, SU, RQ குறுக்குகள் U இல் சந்திக்கின்றன. 2. பரப்பளவு தொடர்பான விதிகள்:

1. **State the problem:** In triangle $\triangle ACD$, sides $AC$ and $AD$ are congruent, so $\triangle ACD$ is isosceles with $AC \cong AD$. Given:

1. **State the problem:** We have an equilateral triangle \(\triangle GHJ\) with sides \(GH = 5x - 13\), \(HJ = 11x - 61\), and \(GJ = 7x - 29\). Since the triangle is equilateral,

1. **Problem Statement:** Find the perimeter of the first shape (a) with given sides. 2. **Given:**

1. **State the problem:** We have a circle with center A, and an arc BC whose length is \(\frac{2}{5}\) of the entire circumference. We need to find the central angle \(x^\circ\) s

1. **State the problem:** We need to find the area of a sector of a circle with radius $9$ cm and central angle $140^\circ$. 2. **Formula for the area of a sector:**

1. Planteamos el problema: Tenemos los puntos $A(2,3)$ y $B(12,7)$ y un punto $P(x,y)$ tal que $PB = 2AP$. 2. Usamos la fórmula de distancia entre dos puntos: $$d = \sqrt{(x_2 - x_

1. **Problem statement:** In triangle ABC, AD and AE are the altitude and median to side BC respectively, with AD = 1 and AE given. It is also given that the angles at A are equal:

1. The problem asks to calculate the value of $n$ and the interior angles of two regular polygons with sides $n-1$ and $n$ respectively, given that the sum of their interior angles

1. **Problem statement:** Given a circle M with diameter length 12 cm, radius $r=6$ cm, and points such that $MC=CB$ and $AC = BC + 1$ cm, find the length of $AB$. 2. **Known facts

1. **Problem:** Given points A (1, 3), B (-2, -1), and C (3, -1), find the coordinates of the vertices of triangle ABC and calculate its area. 2. **Vertices:** The vertices are giv

1. **State the problem:** We need to find the distance between two points $A$ and $B$ on a Cartesian plane. 2. **Formula:** The distance between points $A(x_1, y_1)$ and $B(x_2, y_

1. **Problem statement:** Find the length $x$ in each right triangle using the Pythagorean theorem, correct to 1 decimal place. 2. **Formula:** For a right triangle with legs $a$,

1. The problem is to draw a cube, which is a three-dimensional geometric shape with six equal square faces. 2. A cube can be represented in 2D by drawing a square and then drawing

1. **State the problem:** We need to find the length of one edge of a cube given its volume is 64 cm³. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is given by:

1. **Problem Statement:** We have two similar triangles ABC and DEF. Given sides are $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm. We need to find the length of side $EF$. 2. **Formula and

1. **State the problem:** We have two similar triangles ABC and DEF. Given sides $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm, we need to find the length of side $EF$. 2. **Recall the prope