MathDB
France TST 2007

Source: Problem 3

May 16, 2007
geometrygeometry proposed

Problem Statement

Let A,B,C,DA,B,C,D be four distinct points on a circle such that the lines (AC)(AC) and (BD)(BD) intersect at EE, the lines (AD)(AD) and (BC)(BC) intersect at FF and such that (AB)(AB) and (CD)(CD) are not parallel. Prove that C,D,E,FC,D,E,F are on the same circle if, and only if, (EF)⊥(AB)(EF)\bot(AB).
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