MathDB
lots of circles

Source: Romanian ROM TST 2004, problem 14

May 24, 2004
geometrycircumcircleratioconcurrencyromania

Problem Statement

Let OO be a point in the plane of the triangle ABCABC. A circle C\mathcal{C} which passes through OO intersects the second time the lines OA,OB,OCOA,OB,OC in P,Q,RP,Q,R respectively. The circle C\mathcal{C} also intersects for the second time the circumcircles of the triangles BOCBOC, COACOA and AOBAOB respectively in K,L,MK,L,M. Prove that the lines PK,QLPK,QL and RMRM are concurrent.
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