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equal segments lead to equal segments (Greece Junior 2013)

Source:

July 14, 2019
geometry

Problem Statement

Let ABCABC be an acute angled triangle with AB<ACAB<AC. Let MM be the midpoint of side BCBC. On side ABAB, consider a point DD such that, if segment CDCD intersects median AMAM at point EE, then AD=DEAD=DE. Prove that AB=CEAB=CE.
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