MathDB

4

Part of 2009 District Round (Round II)

Problems(1)

Czech republic,district round,2009,problem 4

Source:

2/18/2012
in an acute triangle ABCABC,DD is a point on BCBC,let QQ be the intersection of ADAD and the median of ABCABCfrom CC,PP is a point on ADAD,distinct from QQ.the circumcircle of CPDCPD intersects CQCQ at CC and KK.prove that the circumcircle of AKPAKP passes through a fixed point differ from AA.
geometrycircumcircleparallelogramgeometry proposed