MathDB
Three lines are concurent

Source: Sharygin contest. The final raund. 2008. Grade 9. Second day. Problem 8

August 31, 2008
geometrycircumcircle

Problem Statement

(J.-L.Ayme, France) Points P P, Q Q lie on the circumcircle ω \omega of triangle ABC ABC. The perpendicular bisector l l to PQ PQ intersects BC BC, CA CA, AB AB in points A′ A', B′ B', C′ C'. Let A" A", B" B", C" C" be the second common points of l l with the circles A′PQ A'PQ, B′PQ B'PQ, C′PQ C'PQ. Prove that AA" AA", BB" BB", CC" CC" concur.
Back to ProblemsView on AoPS