MathDB
A,D,F,E are concylic

Source: Baltic Way 2006

December 4, 2010
geometrycircumcirclegeometry proposed

Problem Statement

In a triangle ABCABC, points D,ED,E lie on sides AB,ACAB,AC respectively. The lines BEBE and CDCD intersect at FF. Prove that if
\color{white}\ . \ \color{black}\   BC^2=BD\cdot BA+CE\cdot CA,
then the points A,D,F,EA,D,F,E lie on a circle.
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