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Diogonals AO, BP and DN are concurrent

Source:

January 11, 2011
geometryparallelogramprojective geometrygeometry proposed

Problem Statement

Through a point OO on the diagonal BDBD of a parallelogram ABCDABCD, segments MNMN parallel to ABAB, and PQPQ parallel to ADAD, are drawn, with MM on ADAD, and QQ on ABAB. Prove that diagonals AO,BP,DNAO,BP,DN (extended if necessary) will be concurrent.
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