Finding a triangle ratio. 
In the triangle ABC, the point P is found on the side AB. AC = 6 cm, AP = 4 cm, AB = 9 cm. Calculate BC:CP.

For some reason, I cannot get this even though I tried for half an hour.
I got that, $BC/CP < 17/10 = 1.7$ by the triangle inequality. $AP/PB = 4/5$
But that does not help one but, I'm very stuck!

The given problem cannot be solved.
If points $P,C,B$ are connected by an elastic rubber band varying angle at $A$ by hinging about $A$ indefinitely many solutions can exist.
EDIT 1/2
It turns out the problem has no $unique$ solution as I originally expected, but is a locus.
EDIT3

Sketched here what I had in mind when I said what I said about locus. It is not relevant to the problem or its solution. However allow me only to say in modest any understanding or context of what we are saying I believe is essential in mathematical considerations.
