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A problem about equal areas

Source: 2000 China Second Round Olympiad P1

August 13, 2019
geometry

Problem Statement

In acute-angled triangle ABC,ABC, E,FE,F are on the side BC,BC, such that ∠BAE=∠CAF,\angle BAE=\angle CAF, and let M,NM,N be the projections of FF onto AB,AC,AB,AC, respectively. The line AEAE intersects ⊙(ABC) \odot (ABC) at DD(different from point AA). Prove that SAMDN=S△ABC.S_{AMDN}=S_{\triangle ABC}.
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