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20 10 Zhuzhou senior high school entrance examination mathematics
Solution: (1)

∫AB//OC

∴∠C=∠BAC

OA = OC

∴∠C=∠OAC

∴∠BAC=∠OAC

That is, the communication is equally divided ∠OAB.

(2)

∵OE⊥AB

∴ AE = be = 1AB= 1。

∠∠AOC = 30,∠ PEA = 90。

∴∠OAE=60

∴∠ EAP = 1 ∠ OAE = 30。

∴ PE = 1PA。

Let PE=x, according to Pythagorean theorem:

The square of x+the square of 65438+0 = the square of (2x) gives the root sign of X=3.

That is, the length of PE is the root number 3 of 3.