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AE - EB=\sqrt{3}, integer computational with circle (2007 HOMC Senior Q5)

Source:

July 18, 2019
geometrycircle

Problem Statement

Suppose that A,B,C,DA,B,C,D are points on a circle, ABAB is the diameter, CDCD is perpendicular to ABAB and meets ABAB and meets ABAB at E,ABE , AB and CDCD are integers and AE−EB=3AE - EB=\sqrt{3}. Find AEAE?
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