Problem 294: Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular. Level: High School, College, SAT Prep.
The figure shows a right triangle ABC inscribed in a circle of center O
(circumcenter). D is the excenter relative to BC and E is the point of
intersection of AD and arc BC. If EF is perpendicular to OB, prove that
DE2 = AC.BF.