Question 3
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 incircles, centered at $O_1$ and $O_2$, meet $AB$ at $P$ and $Q$ respectively. It is known that the area of $\triangle ABC$ is six times the area of the quadrilateral $PQO_2O_1$, determine the possible values of $\frac{AC+BC}{AB}$. Justify your claim.