📐 geometry

1. **Problem:** Draw a triangle with inradius 3 cm and two angles 50° and 70°. 2. **Formula and rules:**

1. The problem is to find the sum of the rhombus, which typically means finding the sum of its diagonals or perimeter depending on context. Here, we clarify the sum of the diagonal

1. **State the problem:** We need to solve for the height $h$ of a cylindrical can given its volume $V = 1188$ cubic inches and the formula for the volume of a cylinder:

1. **Nêu bài toán:** Cho tam giác $\triangle ABC$ với $AB < AC$. Kẻ tia phân giác $AD$ của góc $BAC$ với $D \in BC$. Trên cạnh $AC$ lấy điểm $E$ sao cho $AE = AB$, trên tia $AB$ lấ

1. **State the problem:** We need to find the value of angle $c$ in a triangle where one interior angle is $24^\circ$ and the exterior angle adjacent to $c$ is $60^\circ$. 2. **Rec

1. المشكلة: لدينا مثلثان متشابهان أ ب ج ≈ د س ص ع 2. المطلوب: إيجاد طول ب ج و س ع

1. **Problem Statement:** Find the perimeter of the base of a rectangular prism where the base edges are 4 cm and 6 cm. 2. **Formula:** The perimeter $P$ of a rectangle is given by

1. **Problem Statement:** Given points A(9, 8), B(12, 4), and C(4, -2), solve the following:

1. **Problem Statement:** We have a 3 × 4 rectangle made of identical sticks. We want to find how many sticks are needed to construct a 40 × 50 rectangle. 2. **Understanding the pr

1. **Stating the problem:** In triangle $\triangle ABC$, we have $AB = BC$, $\angle ABC = 40^\circ$, and $\angle GAC = 40^\circ$. We need to find the value of $\angle DGC$. 2. **Un

1. **Stating the problem:** Given a triangle with angles \(\angle D = 134^\circ\) (exterior angle), \(\angle A = 62^\circ\), and \(\angle B = 25^\circ\), find the unknown interior

1. **Problem statement:** We have a circular island centered at $P(0,0)$ with radius 8 km. Four pirates want to divide the island into four equal areas by placing their bases so th

1. **Problem Statement:** Given triangle ABC with point D above BC such that AB = BD, BD is perpendicular to AC, and angles at A, D (near B), and C are labeled $x^\circ$, $x^\circ$

1. **Nêu bài toán:** Cho hình vuông ABCD, điểm E, F lần lượt thuộc các cạnh BC và DC sao cho \( \angle CAE = \angle DAF \). Chứng minh rằng EA là phân giác của \( \angle BEF \). 2.

1. Problem: Oblicz obwód trójkąta równoramiennego, jeśli opisany na nim okrąg ma promień $R=13$ cm, a wysokość poprowadzona do podstawy wynosi: a) $h=20$ cm

1. **State the problem:** Find the surface area of a sphere given its radius $r$. 2. **Formula:** The surface area $A$ of a sphere is given by the formula:

1. Stwierdzenie problemu: Obliczamy obwód trójkąta równoramiennego, gdy znany jest promień okręgu opisanego $R=13$ cm oraz wysokość $h$ opuszczona na podstawę. 2. Wzory i zasady:

1. The problem is to understand the classification and properties of parallelograms. 2. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

1. **Problem Statement:** In triangle $\triangle ABC$, $BM$ and $CN$ are perpendiculars from vertices $B$ and $C$ respectively onto any line passing through $A$. $L$ is the midpoin

1. **Stating the problem:** We have a large rectangle divided into 9 smaller rectangles. The perimeters of rectangles A, B, and C are given as 10 cm, 20 cm, and 30 cm respectively.

1. ננסח את הבעיה: נתונה קובייה עם צלעות $AB = u$, $BC = v$, ו-$CC' = w$. נקודות $E$, $F$, ו-$G$ מוגדרות כפי שבסעיף א'. בסעיף ב' נדרש לחשב את הערך של $\lambda$ כך ש-$\angle EFG = 45