📐 geometry

1. **State the problem:** We need to find the translation components that map the original shape to the transformed shape. 2. **Identify the translation components:** The problem s

1. **State the problem:** We are given a point $P = (-3, -4)$ and a translation that moves $P$ to a new point $P'$. We need to find the translation components and the coordinates o

1. **State the problem:** We need to find the area of a truck shaped like a circular ring (annulus) with an inner radius of $58$ years and an outer radius of $63$ years. 2. **Formu

1. **State the problem:** Determine if the line $\overline{QR}$ with equation $5y = -4x + 41$ is tangent to Circle $O$ at point $R(4,5)$. 2. **Rewrite the line equation in slope-in

1. **State the problem:** We need to find the volume $V$ of a pyramid with given dimensions. 2. **Identify the formula:** The volume of a pyramid is given by $$V = \frac{1}{3} B h$

1. **Problem Statement:** We need to construct $\triangle ABC$ where $AB = 5cm$, $DC = 5cm$, and $D$ is the midpoint of $AB$. We want to find the lengths of $AC$ and $BC$.

1. **State the problem:** We need to construct a 90° angle on a line segment $AB$ where $AB = 7$ cm. 2. **Draw the line segment:** Draw a straight line segment $AB$ of length $7$ c

1. **مشكلة:** لدينا دائرة مع نقاط $C$, $A$, $B$, $D$ على المحيط ونقاط خارجية $E$ و $F$. الزوايا المعطاة هي $30^\circ$ عند $F$ و $60^\circ$ عند $E$. المطلوب هو إيجاد قياس زاوية معين

1. **State the problem:** We need to find the area of a triangle. 2. **Formula for the area of a triangle:** The area $A$ of a triangle can be found using the formula:

1. **State the problem:** We need to find the area of a triangle given its vertices on a grid. 2. **Formula for the area of a triangle:** The area $A$ of a triangle with base $b$ a

1. **State the problem:** We need to find the area of a triangle shown on a square grid. 2. **Formula for the area of a triangle:** The area $A$ of a triangle with base $b$ and hei

1. **State the problem:** We need to find the area of a triangle given its vertices on a coordinate grid. 2. **Identify the vertices:** From the description, the triangle's vertice

1. **সমস্যা বর্ণনা:** আমাদের কাছে একটি আয়তাকার ক্ষেত্র ABCD আছে যার দৈর্ঘ্য $16$ মিটার এবং প্রস্থ $10$ মিটার। ক্ষেত্রের মধ্যে দুটি সমকোণী ত্রিভুজ $\triangle BEF$ এবং $\triangle DH

1. **Problem statement:** Given isosceles triangle ABC with AB = AC = 17 and BC = 16, M and N midpoints of BC and AB, O the circumcenter on AM, and R = AO the circumradius. 2. **St

1. **Problem statement:** Given isosceles triangle ABC with $AB=AC=17$ and $BC=16$, points $M$ and $N$ are midpoints of $BC$ and $AB$ respectively, $O$ is the circumcenter on segme

1. Problem: Given isosceles triangle ABC with AB = AC = 17 and BC = 16, find properties of centers and segments. 2. (a) Since O is the circumcenter, it lies on the perpendicular bi

1. **Problem statement:** Given isosceles triangle ABC with AB = AC = 17 and BC = 16, points M and N midpoints of BC and AB, O the circumcenter on segment AM, and R = AO the circum

1. **Nyatakan masalah:** Kita ada dua segi empat tepat, JKLM (dalam) dan PQRS (luar). JKLM berukuran $12\text{ cm} \times 10\text{ cm}$.

1. **State the problem:** We are given a bird-like figure composed of 7 shapes with specified vertices. We need to perform three transformations on the entire figure: translate 20

1. **State the problem:** We have a tunnel with a semicircular cross-section of diameter $10$ m. A bus is $2$ m from one side of the tunnel, and its roof just touches the tunnel's

1. **Задача:** Знайти об'єм піраміди, основа якої — прямокутний трикутник з кутом $15^\circ$, бічні ребра нахилені до площини основи під кутом $60^\circ$, а радіус описаної кулі до