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BE = AD if DE// AB , CE // BM, D in median BM

Source: 2010 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 26, 2021
geometryequal segmentsparallelUkraine Correspondence

Problem Statement

An arbitrary point DD was marked on the median BMBM of the triangle ABCABC. It is known that the point DE∥ABDE\parallel AB and CE∥BMCE \parallel BM. Prove that BE=ADBE = AD
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