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1999 China Second Round Geometry

Source: 1999 China Second Round Olympiad P1

August 28, 2019
geometry

Problem Statement

In convex quadrilateral ABCD,∠BAC=∠CAD.ABCD, \angle BAC=\angle CAD. EE lies on segment CDCD, and BEBE and ACAC intersect at F,F, DFDF and BCBC intersect at G.G. Prove that ∠GAC=∠EAC.\angle GAC=\angle EAC.
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