Let AC=x and OC=y, then BC=x, AB=2x, OA=√(AC? +OC？ )=√(x？ +y？ )
From pa Pb = 4
(PB+2x) PB=4
Namely PB? +2x PB-4=0
The solution is PB=√(x? +4)-x
∴PC=PB+BC=√(x？ +4)
At △ police, CP⊥OC, and then
CP？ +OC？ =OP？
That is, (x? +4)+y？ =9
X? +y？ =5
∴OA=√(x？ +y？ )=√5