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cyclic trapezoid with perpendicular diagonals, area between circles wanted

Source: Austrian Federal Competition For Advanced Students 2004, Part 2, p3

August 30, 2019

geometrytrapezoidareaperpendiculardiagonalscircles

Problem Statement

A trapezoid

ABCD

with perpendicular diagonals

AC

and

BD

is inscribed in a circle

k

. Let

k_a

and

k_c

respectively be the circles with diameters

AB

and

CD

. Compute the area of the region which is inside the circle

k

, but outside the circles

k_a

and

k_c