$\vartriangle ABC$ is a triangle and $I_b. I_c$ its excenters opposite to $B,C$. Prove that $\vartriangle ABC$ is right at $A$ if and only if its area is equal to $\frac12 AI_b \cdot AI_c$.
Source: 2013 Saudi Arabia Pre-TST 2.4
Tags: geometry, excenter, area of a triangle
$\vartriangle ABC$ is a triangle and $I_b. I_c$ its excenters opposite to $B,C$. Prove that $\vartriangle ABC$ is right at $A$ if and only if its area is equal to $\frac12 AI_b \cdot AI_c$.