Richard and Cylinder

Richard loves Geometry. One day he was playing with a rectangle and a cylinder and came up with a problem. There is a rectangle with sharp edges, kept in an x-y coordinate system. And there is also a cylinder of height 2 units (One unit above the x-y plane and one unit below x-y plane) placed vertically in the same x-y coordinate system. Richard is going to insert a pin in any of the four corner