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equilateral wanted, DE//AC, AE: BE = 2: 1

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist G1 day1

September 23, 2021
geometrycircumcircle

Problem Statement

Let △ABC\vartriangle ABC be isosceles with AB=ACAB = AC. Let ω\omega be its circumscribed circle and OO its circumcenter. Let DD be the second intersection of COCO with ω\omega. Take a point EE in ABAB such that DE∥ACDE \parallel AC and suppose that AE:BE=2:1AE: BE = 2: 1. Show that △ABC\vartriangle ABC is equilateral.
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