MathDB
if 4 circumcircles ae concurrent, then other 4 circumcircles ae concurrent

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P20

August 1, 2018
geometrycircumcircleconcurrencyconcurrentcircles

Problem Statement

A quadrilateral KLMNKLMN is given. A circle with center OO meets its side KLKL at points AA and A1A_1, side LMLM at points BB and B1B_1, etc. Prove that if the circumcircles of triangles KDA,LAB,MBCKDA, LAB, MBC and NCDNCD concur at point PP, then a) the circumcircles of triangles KD1A1,LA1B1,MB1C1KD_1A_1, LA_1B_1, MB_1C_1 and NC1D1NC1D1 also concur at some point QQ; b) point OO lies on the perpendicular bisector to PQPQ.
Back to ProblemsView on AoPS