The following method will work but I'll keep looking for a quicker way.

You're right about AB being a diameter so I've marked the centre as O, and there are lots of radii that must therefore be 2.5 long.

In my diagram I have also marked the midpoints of AC as D and of PC as E.

Triangles OAC and separately POC, are isosceles and the lines from O to those midpoints will cut each isosceles triangle down the middle. That means there will be a right angled triangle in each half.

Now lots of trigonometry.

Use acos(2/2.5) to get angle OCD and hence calculate angle OCE.

Now you can use that to calculate EC and double this to get PC.

Bob

]]>This is pretty hard. I got to where AB is a diameter (ACB is 90 degrees) and the radius is 2.5, but what next?

thanks! ]]>