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Part of 2010 Bosnia and Herzegovina Junior BMO TST

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Bosnia and Herzegovina JBMO TST 2010 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2010

9/17/2018
Points MM and NN are given on sides ADAD and BCBC of rhombus ABCDABCD, respectively. Line MCMC intersects line BDBD in point TT, line MNMN intersects line BDBD in point UU, line CUCU intersects line ABAB in point QQ and line QTQT intersects line CDCD in PP. Prove that triangles QCPQCP and MCNMCN have equal area
geometryequal arearhombus