1, (Experimental Zone of Guangdong Province in 2006) As shown in the figure, in the plane rectangular coordinate system, the quadrilateral is an isosceles trapezoid, and the points,, are moving points on the axis, and the points do not coincide with each other. Connect and pass through the point.
(1) Find the coordinates of this point;
(2) When the point moves at any position, it is an isosceles triangle, and the coordinates of the point are found;
(3) When the point moves at any position, the coordinates of the point at this time are made and calculated.
1, solution: (1) A little work, a little vertical foot,
The quadrilateral is an isosceles trapezoid,
,
Yes,
,
.
, the coordinates of the point,
(2) isosceles triangle,
This is an equilateral triangle.
,
The point is on the axis,
The coordinates of the point or.
(3) and.
,
,
.
, set, that is.
The coordinates of this point.
2. (Suqian City, Jiangsu Province, 2006) Let the center A of a square with a side length of 2a be on the straight line L, the opposite side of the square is perpendicular to the straight line L, the center O of ⊙ O with a radius of r moves on the straight line L, and the distance between point A and point O is d. 。
(1) As shown in Figure ①, when r < a, fill in the common divisor of ⊙O and square according to the relationship between D and A and R.
Enter the following table:
Common points of the relationship between d, a and R.
d>a+r
d=a+r
a-r