1. The points B, D are the endpoints of the other diagonal. The diagonals intersect at the midpoint of AC:

2. The points B, D are placed on the perpendicular bisector of AC:

Calculate the slope of AC:

Therefore the slope of BD is:

3. The points BD are connected by the straight line:

4. The distances

and

must be equal. To get the coordinates of B you need a parallel to AC which have the distance

from AC.

Or:

B is the point of intersection between the perpendicular bisector of AC and the circle around M with radius

:

I've got: (5, 6), (3, 0)