Hanoi Open Mathematics Competition 2012 Senior Question 9

Let \(P\) be the common point of the three internal bisectors of triangle \(ABC\). The line through \(P\) perpendicular to \(CP\) meets \(AC,BC\) at \(M,N\), respectively. If \(AP=3\text{ cm}\), \(BP=4\text{ cm}\), compute \(AM/BN\).