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OPM 2005 Problem 5

  • Final day 2

Considers a quadrilateral [ABCD][ABCD] that has an inscribed circle and a circumscribed circle. The sides [AD][AD] and [BC][BC] are tangent to the circle inscribed at points EE and FF , respectively. Prove that AE⋅FC=BF⋅EDAE \cdot F C = BF \cdot ED . Image

Dataset text AI-MO AoPS. Quoted with source.

Official text: Portuguese Mathematical Olympiad 2005 official paper, page 1.

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