Problem

Source: 2008 Indonesia TST stage 2 test 3 p1

Tags: geometry, incenter, cyclic quadrilateral



Let $ABCD$ be a cyclic quadrilateral, and angle bisectors of $\angle BAD$ and $\angle BCD$ meet at point $I$. Show that if $\angle BIC = \angle IDC$, then $I$ is the incenter of triangle $ABD$.