Problem 325. Isosceles triangle, Altitude, Cevian, Incircle, Excircle.
Level: High School, SAT Prep, College geometry.
The figure shows an isosceles triangle ABC
with AB = BC. AH is an altitude and D is a point on AC. The incircle of
triangle ABD and the excircle of triangle BDC, relative to CD, are equal
circles with radius r, Prove that AH = 4.r