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Prove ∠BCD=2∠KPN

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,812
Let $ABCDEF$ be a convex hexagon such that $AB+DE=BC+EF=FA+CD$ and $AB$ // $DE$, $BC // EF$ and $CD$ // $AF$. Let the midpoints of the sides $AF,\,CD,\,BC$ and $EF$ be $M,\,N,\,K$ and $L$ respectively and let $MN$ meets $KL$ at $P$. Show that $\angle BCD=2\angle KPN$.