The workbook contains code for 2 User Defined Functions array functions which output the intersection points between a Circle and either another Circle or a line.

IntersectLineCircle:

=IntersectLineCircle( LineCoordinates , CircleX , CircleY , Radius )

LineCoordinates is a 2 column range which contains the x and y points for a line.

CircleX is the X position of the circles center point. Can be a value or range reference.

CircleY is the Y position of the circles center point. Can be a value or range reference.

Radius is the radius of the circle. Can be a value or range reference.

The function returns an array of X and Y intersect points. As the number of possible intersect points between a line and circle has a maximum of 2 points the size of the array formula can be determined from the input information. The number of possible intersections is (Line segments-1)*2

IntersectCircleCircle:

=IntersectCircleCircle( Circle1X , Circle1Y , Radius1 , Circle2X , Circle2Y , Radius2 )

Circle1X and Circle2X are the X position of the circles center point. Can be a value or range reference.

Circle1Y and Circle2Y are the Y position of the circles center point. Can be a value or range reference.

Radius1 and Radius2 are the radius of the circle. Can be a value or range reference.

The function returns an array of 2 X and Y intersect points.  

Remember when using array formula to commit the formula with CTRL + SHIFT + ENTER

The download contains both example charts and associated data sets and required vba code.

Tested in xl2007