MathDB
triangle area criterion for right triangle with excenters, 1/2 AI_b AI_c.

Source: 2013 Saudi Arabia Pre-TST 2.4

September 13, 2020
geometryexcenterarea of a triangle

Problem Statement

△ABC\vartriangle ABC is a triangle and Ib.IcI_b. I_c its excenters opposite to B,CB,C. Prove that △ABC\vartriangle ABC is right at AA if and only if its area is equal to 12AIb⋅AIc\frac12 AI_b \cdot AI_c.
Back to ProblemsView on AoPS