inradius http://sphotos-a.ak.fbcdn.net/hphotos-ak-ash4/603253_4699189150138_1902686882_n.jpg
Inside triangle ABC there are three circles with radius $r_1$, $r_2$, and $r_3$ each of which is tangent to two sides of the triangle and to its incircle with radius r. All of $r$, $r_1$, $r_2$, and $r_3$ are distinct perfect square integers. Find the smallest value of inradius $r$.