Question 9
A circle is inscribed in $ABCD$. $AB$ is parallel to $CD$, and $BC = AD$. The diagonals $AC$, $BD$ meet at $E$. The circles inscribed in $ABE$, $BCE$, $CDE$, $DAE$ have radius $r_1$, $r_2$, $r_3$, $r_4$ respectively. Prove that $1 / r_1 + 1 / r_3 = 1 / r_2 + 1 / r_4$.