New posts in triangles

A triangle determinant that is always zero

geometry trigonometry contest-math determinant triangles

Given triangle ABC with $\alpha=2\beta$ and $b, c, a$ is forming an arithmetic sequence. Find $\alpha, \beta, \gamma$.

trigonometry triangles arithmetic arithmetic-progressions

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

inequality contest-math euclidean-geometry triangles geometric-inequalities

How do you derive that the inradius in a right triangle is $r=\frac{a+b-c}2$?

geometry euclidean-geometry triangles circles plane-geometry

$\triangle ABC$ with a point $D$ inside has $\angle BAD=114^\circ$, $\angle DAC=6^\circ$, $\angle ACD=12^\circ$, and $\angle DCB=18^\circ$.

algebra-precalculus trigonometry euclidean-geometry triangles plane-geometry

Where does the $-2ab$ term come from in the cosine law?

geometry trigonometry triangles

Show that the three medians of a triangle are concurrent at a point

geometry proof-verification triangles

How to prove the property of the Lemoine point of a triangle?

optimization triangles median

The position of a ladder leaning against a wall and touching a box under it

geometry euclidean-geometry triangles

Trouble understanding a geometry problem involving triangle and bisector.

geometry euclidean-geometry triangles

Midpoints and other constraints in triangle

geometry euclidean-geometry triangles

Elliptical version of Pythagoras’ Theorem?

geometry euclidean-geometry triangles conic-sections geometric-construction

Why is the inradius of any triangle at most half its circumradius?

geometry euclidean-geometry triangles

A conjecture about the sum of the areas of three triangles built on the sides of any given triangle

geometry euclidean-geometry triangles geometric-construction

Finding the largest triangle inscribed in the unit circle

geometry optimization circles triangles area

I think I see mysterious lines inside triangles—how to prove their existence?

geometry triangles

How to find surface normal of a triangle

geometry triangles

Consider a right angled $\triangle PQR$ right angled at $P$ i.e ($\angle QPR=90°$) with side $PR=4$ and area$=6$.

geometry triangles area rotations

Can Three Equilateral Triangles with Sidelength $s$ Cover A Unit Square?

geometry optimization triangles combinatorial-geometry

What is so special about triangles?!

geometry triangles