Questions tagged [triangles]

Question 1

The goal is to find the point $M$ inside a given right triangle $ABC$ such that $\operatorname{Area}(APMN)=\operatorname{Area}(CQMP)=\operatorname{Area}(BQMN)$, where $N$, $P$, and $Q$ are the ...

Question 2

The Wikipedia article on the Snellius-Pothenot Problem has a section titled "Geometric Solution" that contains a major mistake. It says "By the inscribed angle theorem the locus of ...

Question 3

I came across a geometry problem from a Chinese Grade 9 math exam that involves a specific type of triangle defined as a "Line-Perpendicular Triangle" (线垂三角形). I am stuck on the construction ...

Question 4

[A triangle ABC circumscribes a circle with center O and radius 4,the point of contact between the incircle and AB is at F and at AC it is E and at BC it is D,the lengths of BD is 6,CD=10, find AE] $$(...

Question 5

Why Version 3.0? In the earlier versions of this conjecture, I focused on triangles whose side lengths are distinct prime numbers. Through the discussion that followed, it became clear that the ...

Question 6

I am trying to solve the question Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A. I have tried to approach the problem from backwards (...

Question 7

Given a right triangle $ABC$ with $\angle A=90°$ and $\angle B=30°$. On the extension of side $CA$, we take point $D$ such that $AD=AC/2$, and on the interior of side $BC$, we take point $E$ such that ...

Question 8

Fifty years ago , when I was in college, our teacher , Mrs Marie -Jo , gave us this homework assignment for the holidays : " Find the two types of triangles such that the square of the diameter ...

Question 9

Please help me solve this "mystery". I see several possible answers online, but no proven and correct one (at least from my point of view). There's a regular octagon. Each pair of vertices ...

Question 10

I found this problem in a French paper translated from Arabic in 1927 by an author named Al Bayrouni . I wonder if it can be found in one of Archimedes' works . Here is the statement : ABC is a ...

Question 11

Problem: Let $ABC$ be an acute triangle and $D$ be the foot of the altitude from $A$ onto $BC$. A semicircle with diameter $BC$ intersects segments $AB, AC$ and $AD$ in the points $F, E$ and $X$, ...

Question 12

I encountered a geometry problem involving a right-angled triangle and several constructed equilateral triangles. I am trying to solve the second part of the problem (Case 2 in the image). Continues ...

Question 13

I am given 3 radii $r_a, r_b, r_c$ and I want to determine the 3 angles $\phi_a,\phi_b,\phi_c$ for which the area of the triangle defined by $\left(r_a\cos(\phi_a),r_a\sin(\phi_a)\right),\,\left(r_b\...

Question 14

From what I've seen, the key characteristic of a rigid framework in a polygon is that the sides of the polygon, once set, force the distance between every pair of vertices to remain constant. Is "...

Question 15

Problem Statement: As shown in the diagram below, we have two equilateral triangles, $\triangle ABC$ and $\triangle ADE$, sharing a common vertex $A$. We construct a line connecting vertices $B$ and $...

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Questions tagged [triangles]

Divide a right triangle into three quadrilaterals of equal area .

Snellius–Pothenot Problem and Antigonal Conjugates

Dissecting a "Line-Perpendicular Triangle" (side ratio 1:2) and finding the distance relationship.

Is my proof wrong? The length of AE seems to be 64/11 but i got 6 [closed]

Radium Rabbit Conjecture, version 3.0: The fractional part of the square of the area of a triangle with odd-integer sides is $\frac{3}{16}$. [closed]

Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A

Prove that triangle BNC is isosceles in a 30-60-90 construction

What is the nature of a triangle for which the square of the diameter of its circumcircle is equal to the sum of the squares of two of its sides?

How many triangles in a regular octagon with all corners connected?

Find a synthetic proof to an old problem .

Prove that $BN=LC$. A geometry problem from the national round of math olympiad.

Find the ratio $\frac{AC}{BC}$ given a specific configuration of equilateral triangles around a right triangle (need Euclidean geometry approach)

Maximizing the area of a triangle

What is the most concise complete definition of a rigid framework?

Find the ratio of side lengths of two equilateral triangles given a midpoint condition

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