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triangles with equal areas

Source: SRMC 2023, P1

December 28, 2023
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezoid with AD∥BCAD\parallel BC. A point MM is chosen inside the trapezoid, and a point NN is chosen inside the triangle BMCBMC such that AM∥CNAM\parallel CN, BM∥DNBM\parallel DN. Prove that triangles ABNABN and CDMCDM have equal areas.
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