KöMaL 2010 B4248

Denote the centres of the escribed circles of a triangle ABC by $O_a$, $O_b$, $O_c$, the centre of the incircle by $I$, and the radius of the circumscribed circle by $R$. Let $A_1$ be the intersection of the perpendiculars dropped from point $O_b$ onto line $AB$and from point $O_c$ onto line $AC$. Show that $A_1 I$=2$R$.