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2006年宁波市中考的压轴题如下已知⊙O过点 D(4,3),点 H 与点 D 关于 y 轴对称,过 H 作⊙O的切线交 y 轴于点 A(如图1).(1)求⊙O的半径;(2)求 sin∠HAO 的值;(3)如图2,设⊙O与 y 轴正半轴交点为 P,点 E,F 是线段 OP 上的动点(与点 P 不重合),连结并延长DE,DF交⊙O于点 B,C,直线 BC 交 y 轴于点 G,若⊿DEF 是以 EF 为底的等腰三角形,试探索 sin∠CGO 的大小怎样变化?请说明理由.
The finale of the 2006 Ningbo entrance exam was known as follows: 过O crossed point D(4,3), point H and point D were symmetric about the y axis, and H crossed the tangent line of ⊙O and crossed the y axis at point A (see Figure 1). (1) Find the radius of ⊙ O; (2) Find the value of sin ∠ HAO; (3) As shown in Fig. 2, set the intersection of 正 O and the positive half shaft of y axis as P, and point E, F is the motion on the line segment OP. Points (do not coincide with point P), link and extend DE, DF intersect O at point B, C, and straight line BC intersect y-axis at point G. If ⊿DEF is an isosceles triangle with EF as the base, try sin∠. How does the size of CGO change? Please explain why.