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Competition mathematics plane geometry problem
(1) Solution: Make CE in E vertical to OA and BF in F vertical to OA.

Because: Quadrilateral OABC is isosceles trapezoid, CE and OA are the height of trapezoid.

In the orsi Rt triangle and the and Rt triangle.

CE=BF

CO=BA

So: Rt triangle OCE is equal to Rt triangle ABF.

So: OE=AF, EF=CB, OC=AB=4.

And because ∠ CEO = 90, ∠ COA = 60 in OCE of Rt triangle.

So: ∠ oce = 30.

So: OE= 1/2CO=2.

So: abscissa of point B =OA-AF=7-2=5.

Ordinate = BF = √ baxba-afxaf = √ 4x4-2x2 = √16-4 = √12 = 2 √ 3.

So: the coordinate of point B is (5,2 √ 3).

(2) solution: suppose that there is a little p that makes ∠ CPO = 60.

The triangle COP is an isosceles triangle,

So: OP=OC=AB=4.

Because: Point P is a point on the X axis.

Therefore, P (4 4,0) conforms to the fact that p is a moving point on the X axis, and the point P is not coincident with the point O and the point A. ..

The hypothesis holds.

So the coordinate of point P is (4,0).