📐 geometry

1. مسئله: نسبت شعاع دایره بزرگ‌تر به شعاع دایره کوچک‌تر را پیدا کنیم، وقتی دایره‌های بزرگ‌تر بر هم مماس‌اند و دایره‌های کوچک‌تر بر دایره‌های بزرگ‌تر مماس‌اند و مرکز دایره‌ها روی رأ

1. **Problem statement:** Given a circle with points N, Q, O on the circumference and points P, R outside the circle, we know that $m\angle Q\hat{N}O = 238^\circ$. We need to find

1. **State the problem:** Given $m\angle N\hat{O} = 238^\circ$, find $m\angle P\hat{O}Q$ and $m\angle P\hat{Q}R$ based on the circle and points described. 2. **Recall circle angle

1. **State the problem:** Daniel needs to paint the walls and ceiling of a cuboidal hall with dimensions length = 15 m, breadth = 10 m, and height = 7 m. Each can of paint covers 1

1. **State the problem:** Find the area of a cuboid. 2. **Formula:** The total surface area $A$ of a cuboid with length $l$, width $w$, and height $h$ is given by:

1. **Problem statement:** Given that $\angle ADC = \frac{1}{2} \angle AOC$ and $\angle ABC = 120^\circ$, find the value of $\angle AOC$. 2. **Formula and rules:** In circle geometr

1. **Problem statement:** Given that $\angle ADC = \frac{1}{2} \angle AOC$ and $\angle ABC = 120^\circ$, find the value of $\angle AOC$. 2. **Understanding the problem:** The probl

1. **Problem statement:** Given triangle ABC with points M on BC, X on AB, Z on AC such that XZ is parallel to BC. Given lengths: AZ = 3 cm, ZC = 2 cm, BM = 3 cm, MC = 5 cm. Find t

1. **Problem Statement:** Find the angle $\angle ADC$ given that $\angle ADB = \angle CDB$ (equal chords subtend equal angles at the circumference) and the circle touches quadrilat

1. **Problem Statement:** We have a parallelogram ABCD with diagonal BD intersecting line segment AE at point F, where E is any point on side BC. We need to prove that $$\frac{DF}{

1. **State the problem:** Given that segment $XM$ bisects segment $AO$ and angle $X$ equals angle $M$, prove that triangles $AXI$ and $OMI$ are congruent. 2. **Identify given infor

1. The problem asks to identify a solid with surfaces that are fully or partially curved. 2. In geometry, solids can have flat surfaces (like cubes) or curved surfaces (like sphere

1. The problem asks: What is a shape with all sides or maximum sides curved called? 2. In geometry, shapes can have straight or curved sides. When a shape has all sides curved, it

1. The problem asks to classify the given quadrilaterals based on their properties. 2. The first figure is a square with two diagonals intersecting at the center. A square is a qua

1. **Problem:** Find the surface area of the L-shaped prism with edges 12 yd, 11 yd vertically, 3 yd along top, and two 4 yd segments horizontally. 2. **Formula:** Surface area of

1. The problem asks to find the surface area of each solid figure shown. 2. The surface area of a solid figure is the total area of all its outer surfaces.

1. **Stating the problem:** Given a circle with center O, radius AO = 21 cm, and central angle \(\angle AOB = 60^\circ\), we want to analyze the properties of segments and arcs rel

1. **State the problem:** We have an isosceles triangle with one angle given as 104° and the two base angles equal, one labeled as $92 - 2x$ degrees. We need to find the value of $

1. **State the problem:** We are given that ray RT bisects angle \(\angle QRS\), meaning it divides \(\angle QRS\) into two equal angles. The measure of \(\angle QRS\) is 122 degre

1. The problem asks for the translation rule that maps segment BC to B'C'. 2. Given points:

1. **Problem statement:** Determine $X$ and $Z$ such that points $A(-1,0,3)$, $B(3,-2,6)$, and $C(X,2,Z)$ are collinear. 2. **Formula and rule:** Three points are collinear if the