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.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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