Problem

Source: VA. Yasinsky Geometry Olympiad 2017 X-XI p3, advanced X-XI p1 [Ukranie]

Tags: geometry, maximum value, area, circle



Given circle $\omega$ and point $D$ outside this circle. Find the following points $A, B$ and $C$ on the circle $\omega$ so that the $ABCD$ quadrilateral is convex and has the maximum possible area. Justify your answer.