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6 points in a parallelogram, two equal segments

Source: JBMO Shortlist 2005

October 13, 2017
geometryparallelogramJBMO

Problem Statement

Let ABCDABCD be a parallelogram. P∈(CD),Q∈(AB)P \in (CD), Q \in (AB), M=AP∩DQM= AP \cap DQ, N=BP∩CQN=BP \cap CQ, K=MN∩AD K=MN \cap AD, L=MN∩BCL= MN \cap BC. Prove that BL=DKBL=DK.
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