AIME II Problem 15 2007

[zefuri]

Four circles [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] with the same radius are drawn in the interior of triangle ABC such that [unparseable or potentially dangerous latex formula] is tangent to sides AB and AC, [unparseable or potentially dangerous latex formula] to BC and BA, [unparseable or potentially dangerous latex formula] to CA and CB, and [unparseable or potentially dangerous latex formula] is externally tangent to [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. If the sides of triangle ABC are 13, 14, and 15, the radius of [unparseable or potentially dangerous latex formula] can be represented in the form [unparseable or potentially dangerous latex formula], where m and n are relatively prime positive integers. Find m+n.

[88bobcat]