Solution: O 1 passes through the center of the circle, O 2 is perpendicular to EO 1 and Fo2, both perpendicular to the straight line AP.

Af = AC/2 and AE = AP/2 are obtained from the vertical longitude theorem of a circle.

EO 1//FO2

AO 1:AO2=AE:AF=3:2

AP:AC=3:2

From the tangent theorem, we know that Pb 2 = PC * PA

PB/PC=PA/PB

So Pb 2 = pa * (pa-AC) = pa * (pa-2pa/3) = pa 2/3.

PA/PB= root number 3

So PB/PC= root number 3

Choose B.