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prove concurrency of lines (altitude and lines such that angles are equal)

Source: 2001 Moldova MO Grade 9 P4

April 12, 2021
geometry

Problem Statement

In a triangle ABCABC the altitude ADAD is drawn. Points MM on side ACAC and NN on side ABAB are taken so that ∠MDA=∠NDA\angle MDA=\angle NDA. Prove that the lines AD,BMAD,BM and CNCN are concurrent.
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