Question 39
A circle with radius $r$ is inscribed in the triangle $ABC$. Circles with radii $r_{1}, r_{2}, r_{3}$ ($r_{1}, r_{2}, r_{3} \lt r$) are inscribed in the angles $A, B, C$ so that each touches the incircle externally. Prove that $r_{1} + r_{2} + r_{3} \geq r$.