Math Forum :: View topic – Geometry Test

Suppose M is a point on the side AB of triangle ABC such that the incircles of triangle AMC and triangle BMC have the same radius. The two circles, centered at O1 and O2, meet AB at P and Q respectively. It is known that the area of triangle ABC is six times the area of the quadrilateral PQO1O2, determine the possible value(s) of (AC+BC)/AB. Justify your claim. It is the forth question of the geometry test. I don’t know how to solve it. Can anyone teach me how to solve it?