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Question

Segment AB is both a diameter of a circle of radius 1 and a side of an equilateral triangle ABC. The circle also intersects AC and BC at points D and E, respectively. The length of AE is

Accepted Answer

Note that since AB is a diameter, AEB = 90^, which means AB is an altitude of equilateral triangle ABC. It follows that ABE is a 30^-60^-90^ triangle, and so AE = AB 32 = (2 1) (32) = 3.