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product AE x AD is independent of the choice of E

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p2b

February 11, 2020
isoscelescircleProductindependentgeometry

Problem Statement

Let A,B,CA,B,C be different points on a circle such that AB=ACAB = AC. Point EE lies on the segment BCBC, and D≠AD \ne A is the intersection point of the circle and line AEAE. Show that the product AE⋅ADAE \cdot AD is independent of the choice of EE.
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