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Regional Olympiad - FBH 2010 Grade 11 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018
geometryangle bisectorareacircumcircle

Problem Statement

Angle bisector from vertex AA of acute triangle ABCABC intersects side BCBC in point DD, and circumcircle of ABCABC in point EE (different from AA). Let FF and GG be foots of perpendiculars from point DD to sides ABAB and ACAC. Prove that area of quadrilateral AEFGAEFG is equal to the area of triangle ABCABC
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