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BD=2CD when <BED=< BAC=2 <CED, AB=AC

Source: Singapore Junior Math Olympiad 2017 2nd Round p3 SMO

March 25, 2020
isoscelesanglesequal segmentsequal angles

Problem Statement

Let ABCABC be a triangle with AB=ACAB=AC. Let DD be a point on BCBC, and EE a point on ADAD such that ∠BED=∠BAC=2∠CED\angle BED=\angle BAC=2\angle CED. Prove that BD=2CDBD=2CD.
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