MathDB

2b

Part of 1997 Abels Math Contest (Norwegian MO)

Problems(1)

product AE x AD is independent of the choice of E

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p2b

2/11/2020
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.
isoscelescircleProductindependentgeometry