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line through incenters forms a triangle with circumcenter of a vertex

Source: Slovenia 1998 4th Grade P3

April 30, 2021
geometryincentercircumcircleTriangle

Problem Statement

In a right-angled triangle ABCABC with the hypotenuse BCBC, DD is the foot of the altitude from AA. The line through the incenters of the triangles ABDABD and ADCADC intersects the legs of △ABC\triangle ABC at EE and FF. Prove that AA is the circumcenter of triangle DEFDEF.
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