Let $ABC$ be a triangle with inscribed radius $r$ and circumscribed radius $R$. Let $A′B′C′$ be the triangle for which $A′B′$ is the perpendicular to $OC$ through $C$ and so on. Let $r_1$ be the inscribed radius of $\triangle A'BC$, $r_2$ be the inscribed radius of $\triangle AB'C$ and so on. Find $r_1+r_2+r_3$ in terms of $r$ and $R$.
Although it seems easy, I haven't been able to make any progress. I understand that the inscribed radius radius of $\triangle A'B'C'$ is $R$, but not much else. Can someone explain me how to do this? :)