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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.


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