Questions tagged [triangles]
For questions about properties and applications of triangles.
7,210 questions
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Dissecting a "Line-Perpendicular Triangle" (side ratio 1:2) and finding the distance relationship.
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 ...
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Is my proof wrong? The length of AE seems to be 64/11 but i got 6
[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]
$$(...
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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]
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 ...
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Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A
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 (...
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Prove that triangle BNC is isosceles in a 30-60-90 construction
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 ...
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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?
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 ...
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How many triangles in a regular octagon with all corners connected?
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 ...
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Find a synthetic proof to an old problem .
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 ...
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Basic Proportionality Theorem/ Thales Theorem [closed]
The Basic Proportionality Theorem seems so obvious but the construction to prove it (drooping perpendicular to equate areas) is not at all obvious to me. Can anyone tell how to prove this Theorem in a ...
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Prove that $BN=LC$. A geometry problem from the national round of math olympiad.
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 $X$, ...
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Find the ratio $\frac{AC}{BC}$ given a specific configuration of equilateral triangles around a right triangle (need Euclidean geometry approach)
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 ...
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Maximizing the area of a triangle
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\...
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What is the most concise complete definition of a rigid framework?
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 "...
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Find the ratio of side lengths of two equilateral triangles given a midpoint condition
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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What is the length of the height AH?
I'm trying to find a problem about right triangles with a minimalist statement that isn't too obvious. Here's what I've come up with :
ABC is an A–right triangle, H is the orthogonal projection of A ...
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