KöMaL 2019 C1544

The diagonals of a circumscribed trapezium $ABCD$ intersect at $E$. The radii of the inscribed circles of triangles $ABE$, $BCE$, $CDE$ and $DAE$ are $r_1$, $r_2$, $r_3$ and $r_4$, respectively. Prove that $\frac{1}{r_1}+\frac{1}{r_3}=\frac{1}{r_2}+\frac{1}{r_4}.$