📐 geometry

1. **Stating the problem:** We have a rectangle ABCD with points E and I outside it. Given lengths are $BE=4$ cm and $AI=8$ cm. We want to analyze the figure and find relationships

1. **State the problem:** Calculate the volume of a cone with base radius $r=5$ cm and curved surface area $A=109.9$ cm$^2$. 2. **Recall formulas:**

1. **Problem Statement:** We have a circle with center $P$ and points $A, B, C, D, E$ on the circle in clockwise order. $\overline{AD}$ and $\overline{BE}$ are diameters. We want t

1. **Problem statement:** Given a semicircle $(O; R)$ with diameter $AB$, $C$ is the midpoint of $AO$. The line through $C$ perpendicular to $AO$ intersects the semicircle at $I$.

1. **Problem statement:** We have two isosceles triangles TSV and UTV with given angles and side equalities. We need to find the values of angles $x$ and $y$. 2. **Given informatio

1. **Énoncé du problème :** Soient ABC un triangle dans le plan (P) et G = bary{(A, 4); (B, 3); (C, 2)}.

1. **Problem statement:** Given circle $(O)$ and point $A$ outside it, with tangents $AB$ and $AC$ touching $(O)$ at $B$ and $C$. $H$ is the intersection of $OA$ and $BC$. 2. **Par

1. **Stating the problem:** We are given four polygons with some angles labeled and asked which angle among \(\angle a, \angle b, \angle c, \angle d\) cannot be found given the ang

1. **Problem statement:** Given a circle $(O)$ and a point $A$ outside the circle. From $A$, two tangents $AB$ and $AC$ are drawn to the circle, touching at points $B$ and $C$ resp

1. **Menentukan volume dan luas permukaan bangun 6 (prisma segiempat dengan prisma segitiga di atasnya)** Diketahui: panjang = 8 cm, lebar = 7 cm, tinggi prisma segiempat = 6 cm, t

1. **Problem statement:** Given right triangle $\triangle ABC$ right-angled at $A$ with $AB < AC$. $M$ is the midpoint of $BC$. $E$ and $F$ are the perpendicular projections of $M$

1. Bạn hỏi liệu tôi có thể giải toán hình và vẽ toán hình không. 2. Tôi có thể giúp bạn giải các bài toán hình học bằng cách sử dụng các công thức, định lý và giải thích chi tiết t

1. **Énoncé du problème :** Nous avons un triangle ABC avec I milieu de [BC]. Le point G est défini comme barycentre $G = \mathrm{Bar} \{(A,-2);(B,1);(C,-1)\}$.

1. **Problem Statement:** We have a stack of 7 identical cubes arranged in a stepped form. We want to find the minimum number of additional cubes needed to complete this stack into

1. The problem involves finding the value of $X$ formed by the intersection of lines $CE$ and $DB$ in a triangle configuration. 2. According to the problem, $CE$ and $DB$ intersect

1. The problem involves a square with side length 4 cm and four quarter circles drawn inside it, each centered at a corner of the square. 2. We want to find the area of the shaded

1. **Problem statement:** We are given a circle with two chords intersecting inside it, forming four angles. One angle is 25°, another is 84°, and we need to find the unknown angle

1. **State the problem:** We are given a circle with center O and two intersecting chords creating angles $x$ and $y$ at the circumference. The central angle between the two points

1. **State the problem:** We need to find the value of $x$ given two angles in a triangle: one angle on the circle is $x + 50$ degrees and the angle at point $O$ inside the triangl

1. The problem is to create an image of stained glass using corresponding equations. 2. Stained glass patterns can be modeled using geometric shapes and trigonometric functions to

1. The problem is to create a stained glass art design using mathematical equations. 2. Stained glass art can be represented by geometric shapes and curves, each described by equat