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Regional Olympiad - FBH 2015 Grade 11 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018
geometryangle bisector

Problem Statement

Let FF be an intersection point of altitude CDCD and internal angle bisector AEAE of right angled triangle ABCABC, ∠ACB=90∘\angle ACB = 90^{\circ}. Let GG be an intersection point of lines EDED and BFBF. Prove that area of quadrilateral CEFGCEFG is equal to area of triangle BDGBDG
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