Solution: connect O 1A, O 1P, O2A, extend the intersection of PA O2 at point E, and connect O2E.

Because o1a = o1p.

So the angle O 1AP= angle O 1PA.

Because O2A=O2E

So angle O2AE= angle O2EA.

Because angle O 1AP= angle O2AE

So angle O 1PA= angle O2EA.

So the triangle OWAP is similar to the triangle OWAE (AA).

So PA/AE=O 1A/O2E.

Because the radius of the circle O 1 is R.

So o1a = R.

Because the radius of circle O2 is r.

So O2E=R

Because r: r = 4: 5.

So PA/AE=4/5.

PA/PE=4/9

Because PB is the tangent of the original O2.

So from the point of view of the tangent line theorem:

PB^2=PA*PE

Because PB=6

So PA=4