Problem

Source: CRMO 2015 region 1 p1

Tags: geometry, circumcircle, incenter, right angle, cyclic quadrilateral



In a cyclic quadrilateral $ABCD$, let the diagonals $AC$ and $BD$ intersect at $X$. Let the circumcircles of triangles $AXD$ and $BXC$ intersect again at $Y$ . If $X$ is the incentre of triangle $ABY$ , show that $\angle CAD = 90^o$.