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20 14 Shenzhen second motorcycle mathematics 15 questions
Point O is OC⊥AP, vertical foot is C, and C is the midpoint of AB.

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