Let ABC be a triangle. Construct three circles k1, k2, and k3 with the same radius such that they intersect each other at a common point O inside the triangle ABC and k1∩k2={A,O}, k2∩k3={B,O}, k3∩k1={C,O}. Let ta be a common tangent of circles k1 and k2 such that A is closer to ta than O. Define tb and tc similarly. Those three tangents determine a triangle MNP such that the triangle ABC is inside the triangle MNP. Prove that the area of MNP is at least 9 times the area of ABC. PuMACIndividual Finalsgeometry