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given cyclic ABCD with metric relations + angle, find radius (Chile 2015 L1 P5)

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May 26, 2019
geometrycyclic quadrilateralradius

Problem Statement

A quadrilateral ABCDABCD is inscribed in a circle. Suppose that ∣DA∣=∣BC∣=2|DA| =|BC|= 2 and∣AB∣=4 |AB| = 4. Let EE be the intersection point of lines BCBC and DADA. Suppose that ∠AEB=60o\angle AEB = 60^o and that ∣CD∣<∣AB∣|CD| <|AB|. Calculate the radius of the circle.
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