MathDB

1

Part of 2013 Korea National Olympiad

Problems(1)

Circumcenters

Source: Korea National 2013 #1

11/10/2013
Let PP be a point on segment BCBC. Q,RQ, R are points on AC,ABAC, AB such that PQ∥ABPQ \parallel AB and PR∥AC PR \parallel AC. O,O1,O2O, O_{1}, O_{2} are the circumcenters of triangle ABC,BPR,PCQABC, BPR, PCQ. The circumcircles of BPR,PCQBPR, PCQ meet at point K(≠P)K (\ne P). Prove that OO1=KO2OO_{1} = KO_{2} .
geometrycircumcirclegeometry proposed