Let $BM$ be the median of the triangle $ABC$, in which $AB> BC$. Point $P$ is chosen so that $AB \parallel PC$ and $PM \perp BM$. Prove that $\angle ABM = \angle MBP$. (Mikhail Standenko)
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Tags: geometry, equal angles, angles
Let $BM$ be the median of the triangle $ABC$, in which $AB> BC$. Point $P$ is chosen so that $AB \parallel PC$ and $PM \perp BM$. Prove that $\angle ABM = \angle MBP$. (Mikhail Standenko)