Question 139
A circle $k$ of radius $r$ is inscribed in $\triangle ABC$. The tangent lines of $k$ that are parallel to sides $AB$, $BC$ and $CA$ intersect the other sides of $\triangle ABC$ at points $M, N$; $P, Q$ and $L, T$, respectively ($P, T \in AB$, $L, N \in BC$ and $M, Q \in AC$). Denote by $r_1, r_2, r_3$ the radii of the circles inscribed in triangles $MNC$, $PQA$ and $LTB$, respectively. Prove that $r_1 + r_2 + r_3 = r$.
**Fig. 28**
**Fig. 28**