Question 99
Given integers $a$, $b$, $c$, with
$$
\frac{a^2}{a^2 + b^2} + \frac{c^2}{a^2 + c^2} = \frac{2c}{b+c},
$$
prove that the product $bc$ is a perfect square.
$$
\frac{a^2}{a^2 + b^2} + \frac{c^2}{a^2 + c^2} = \frac{2c}{b+c},
$$
prove that the product $bc$ is a perfect square.