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
DE^{2} = AC.BF.

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