What intersection? You kind of glossed over that. I will presume that you want the center of the sphere placed on the exposed corner of the square sitting on the rectangle.
Of course, if you have a guide point at the center of the sphere and you use X-Ray Face style, you can just snap point to point. However, you can always position an object with great precision along each axis in turn, using inferencing to align some appropriate surface feature in each direction. In this case, turn hidden geometry on so you have plenty of on-center points to choose from. For example: