How can one go about solving the following problem?
Inscribe a circle in an arbitrary triangle. Call it's radius $r_1$. Inscribe three more circles so that each one is tangent to two sides of the triangle and the first circle (i.e., each at a different corner). Call the radii $r_2, r_3, r_4$. Find a relationship between $r_1, r_2, r_3$ and $r_4$.
The most promising method of attack for me was to consider the isosceles triangles at each corner: the base being the tangent line to the point of intersection of the angle bisector of the triangle and the first circle. But I'm stuck.
Any suggestions much appreciated.