Prove the Condition for Construction of a Triangle
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 $pa^2+qb^2 > pqc^2$
40596
Proving a relation between inradius ,circumradius and exradii in a triangle
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
77576
Using the triangle inequalities to prove a bound in the complex plane
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
139065
Proving $\csc\frac\alpha2+\csc\frac\beta2+\csc\frac\gamma2 \ge 6$, where $\alpha$, $\beta$, $\gamma$ are the angles of a triangle
143968
Proving this inequality by mathematical induction
12646
In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$
112740
Prove the triangle is equilateral given that a quadrilateral related to its circumcircle is a kite
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} $
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
128786
How to use triangle inequality to establish Reverse triangle inequality
94091
In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
89452
Proof about Graph with no triangle
73392
How to prove that triangle inscribed in another triangle (were both have one shared side) have lower perimeter?
97059
How to prove the property of the Lemoine point of a triangle?
97584
How to prove this property using convexity?