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China South East Mathematical Olympiad 2021 Grade10 P6

Source:

July 30, 2021
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Let EE be a point on side BC,BC, FF be a point on side AE,AE, GG be a point on the exterior angle bisector of ∠BCD,\angle BCD, such that EG=FG,EG=FG, ∠EAG=12∠BAD.\angle EAG=\dfrac12\angle BAD. Prove that AB⋅AF=AD⋅AE.AB\cdot AF=AD\cdot AE.
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