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Solve junior high school math problems
Solution: (1) cross c is CM⊥x axis, vertical foot m, cross b is BN⊥x axis, vertical foot n.

Because the quadrilateral OABC is an isosceles trapezoid, AB = 4, ∠ COA = 60.

Therefore: OC=AB=4, ∠ OAB = 60, AN=OM, CM=BN.

So: OM= 1/2? OC=2=AN,CM=2√3=BN

Because BC//OA, OA=7

Therefore: MN=OA-OM-AN=3.

Therefore: ON=OM+MN=5.

Therefore: b (5 5,2 √ 3)

(2) If △OCP is an isosceles triangle, because ∠ COA = 60.

Then: △OCP is a regular triangle or P is on the negative semi-axis of the X axis.

① When △OCP is a regular triangle,

Therefore: OP=OC=4.

Therefore: p (4 4,0)

② When P is on the negative semi-axis of the X-axis

And OP=OC=4.

Therefore: p (-4,0)

(3)CPD =∠OAB =∠COA = 60

Therefore: ∠ OPC+∠ DPA = ∠ DPA+∠ ADP = 120.

Therefore: ∠OPC=∠ADP.

Therefore: △OPC∽△ADP

Therefore: OP/AD=OC/PA.

Because 8*BD=5*AB, AB=4.

Therefore: BD=5/2.

Therefore: AD=AB-BD=3/2.

Let OP =x, so: pa = OA-op = 7-X.

Therefore: x/(3/2)=4/(7-x)

So: x= 1 or x=6.

Therefore: p (1, 0) or p (6, 0)