Ramesh and Reena are playing with triangle ABc. Ramesh draws a line that bisects ∠BAC; this line cuts BC at d. Reena then extends AD to a point P. In response, Ramesh joins B and P. Reena then announces that BD bisects ∠PBA, what a surprise! Together, Ramesh and Reena find that BD= 6 cm, AC= 9 cm, DC= 5 cm, BP= 8 cm, and DP = 5 cm. How long is AP?