- If has inradius and semi-perimeter , then the area of is . This formula holds true for other polygons if the incircle exists.
Add in the incircle and drop the altitudes from the incenter to the sides of the triangle. Also draw the lines , and . After this AB, AC, and BC are the bases of , and respectively. But they all have the same height(the inradius), so .
- Verify the inequality .
- Verify the identity (see Carnot's Theorem).
- 2007 AIME II Problems/Problem 15
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