MathDB
a condition for 4 points to be concyclic

Source: China second round 2007 p1

March 10, 2012
geometrypower of a point

Problem Statement

In an acute triangle ABCABC, AB<ACAB<AC. ADAD is the altitude dropped onto BCBC and PP is a point on ADAD. Let PE⊥ACPE\perp AC at EE, PF⊥ABPF\perp AB at FF and let J,KJ,K be the circumcentres of triangles BDF,CDEBDF, CDE respectively. Prove that J,K,E,FJ,K,E,F are concyclic if and only if PP is the orthocentre of triangle ABCABC.
Back to ProblemsView on AoPS