MathNet 1996 — Part 01 Question 17

Let $ABCD$ be a cyclic convex quadrilateral and let $r_{a}, r_{b}, r_{c}, r_{d}$ be the radii of the circles inscribed in the triangles $BCD$, $ACD$, $ABD$, $ABC$ respectively. Prove that $r_{a} + r_{c} = r_{b} + r_{d}$.