An arbitrary point $D$ was marked on the median $BM$ of the triangle $ABC$. It is known that the point $DE\parallel AB$ and $CE \parallel BM$. Prove that $BE = AD$
Problem
Source: 2010 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7
Tags: geometry, equal segments, parallel, Ukraine Correspondence