A cyclic quadrilateral $ABCD$ is given. Let $I{}$ and $J{}$ be the centers of circles inscribed in the triangles $ABC$ and $ADC$. It turns out that the points $B, I, J, D$ lie on the same circle. Prove that the quadrilateral $ABCD$ is tangential.
Problem
Source: Russian TST 2016, Day 11 P1 (Group A), P2 (Group B)
Tags: geometry, cyclic quadrilateral, tangential quadrilateral