Is the outer center of an equilateral triangle, 1 point.

Central angle.

When it is not perpendicular to the vertical, the vertical feet are respectively.

By, and,

, .

. 1 point

. 1 point

The point is on the bisector of. 1

When.

That is to say, the point is on the bisector of.

To sum up, a point moving on a ray is on the bisector.

(2) Solution: As shown in Figure 5,

Average distribution,

. 1 point

From (1),,,

, .

,. 1 point

.

... 1 point

The domain is:. 1.

(3) Solution: ① As shown in Figure 6, when tangent to the circle,; 2 points

② As shown in Figure 7, when tangent to the circle,; 1 point

③ As shown in Figure 8, when tangent to the circle, score .2.