Prove that $r^2+ r_1^2+ r_2^2 +r_3^2=16R^2-a^2-b^2-c^2$
Prove $r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$ for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, exradii $r_1$, $r_2$, $r_3$