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Bosnia and Herzegovina JBMO TST 2010 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2010

September 17, 2018
geometryequal arearhombus

Problem Statement

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
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