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circle with diameter the altitude

Source: Nordic Mathematical Contest 1996 #3

October 4, 2017
geometryaltitude

Problem Statement

The circle whose diameter is the altitude dropped from the vertex AA of the triangle ABCABC intersects the sides ABAB and ACAC at DD and EE, respectively (AD,AE)(A\ne D, A \ne E). Show that the circumcenter of ABCABC lies on the altitude drawn from the vertex AA of the triangle ADEADE, or on its extension.