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computational with isosceles trapezoid, inscribed, <DAE=90^o, AE /AB=3/4

Source: 2016 (-17) Swedish Mathematical Competition p3

August 31, 2020
geometrytrapezoidisoscelescircumcircle

Problem Statement

The quadrilateral ABCDABCD is an isosceles trapezoid, where AB∥CDAB\parallel CD. The trapezoid is inscribed in a circle with radius RR and center on side ABAB. Point EE lies on the circumscribed circle and is such that ∠DAE=90o\angle DAE = 90^o. Given that AEAB=34\frac{AE}{AB}=\frac34, calculate the length of the sides of the isosceles trapezoid.
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