1. The perimeter of a triangle is 12 and its inradius is 1. What is the area of the triangle?
2. is the incenter of Triangle ABC. We have CE=12, AE=9, and AB=12. Find BC.
1. We can assume that the triangle is equilateral, so the area is sqrt(3)/4*(12/2)^2 = 9 sqrt(3).
2. From similar triangles, BC = (12 + 12)/(12 + 9)*12 = 96/7.