proof involving a triangle with a point inside it.
73392
How to prove that triangle inscribed in another triangle (were both have one shared side) have lower perimeter?
37744
Prove that given $a,b,c > 0$, it is possible to construct a triangle with sides of length $a,b,c$ if and only if $pa^2+qb^2 > pqc^2$
145466
Is this a valid mathematical proof?
46353
Proof that $\cos(\pi/3)=1/2$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
58932
Hard contest type trigonometry proof
41907
Triangulation of a simple polygon (elementary proof?)
6335
Proving that the set enclosed by an ellipse is convex
145783
How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?
88605
Proof of the Reverse Triangle Inequality
97473
Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$
94091
In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
112740
Prove the triangle is equilateral given that a quadrilateral related to its circumcircle is a kite
7164
Proof of Darboux's theorem
73029
If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $
30044
Inequality with triangle sides
103416
Proving area under curve