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Circumcenter lies on EF

Source: Bosnian TST, 2008, 2.nd day

May 18, 2008
geometrycircumcircletrigonometrypower of a pointradical axisgeometry proposed

Problem Statement

Let AD AD be height of triangle △ABC \triangle ABC and R R circumradius. Denote by E E and F F feet of perpendiculars from point D D to sides AB AB and AC AC. If AD\equal{}R\sqrt{2}, prove that circumcenter of triangle △ABC \triangle ABC lies on line EF EF.
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