Hi, here is my problem:

Inside of a triangle $\displaystyle ABC$, a random point $\displaystyle M$, in which three straight lines parallel to the respective sides of the triangle intersect, was chosen. Those straight lines have divided the triangle into six parts, three of which are also triangles. Let $\displaystyle r_1, r_2, r_3$ be the radii of circles inscribed in those three triangles, and let $\displaystyle r$ be the radius of a circle inscribed in triangle $\displaystyle ABC$. Show that $\displaystyle r=r_1+r_2+r_3$.

Help appreciated. Thank you.