SE-SKOLORNAS 2016 Problem 3

The quadrilateral $ABCD$ is an isosceles trapezoid, where $AB\parallel CD$ . The trapezoid is inscribed in a circle with radius $R$ and center on side $AB$ . Point $E$ lies on the circumscribed circle and is such that $\angle DAE = 90^o$ . Given that $\frac{AE}{AB}=\frac34$ , calculate the length of the sides of the isosceles trapezoid.