Let A B C be a triangle. Construct three circles k_{1}, k_{2} and k_{3} with the same radius such that they intersect each other at a common point O inside the triangle A B C and k_{1} \cap k_{2}=\{A, O\}, k_{2} \cap k_{3}=\{B, O\}, k_{3} \cap k_{1}=\{C, O\}. Let t_{a} be a common tangent of circles k_{1} and k_{2} such that A is closer to t_{a} than O. Define t_{b} and t_{c} similarly. Those three tangents determine a triangle M N P such that triangle A B C is inside the triangle M N P. Prove that the area of M N P is at least 9 times the area of A B C.