Tangent parallel squares centered on circumference of circle

Touching, parallel squares centered on circumference of circle
Two square of the same width W have corresponding sides parallel and centers on a circle of radius one. The square meet along a line which lies a distance D from the center of the circle. Depending upon the size of the angle ABK and the distance D, find the range of values of W, the value of angle ABK and D (if they exist) for which the two squares touch at only one corner or for which the two squares touch at two corners. If, for some values of angle ABK and D the squares "overlap" (i.e. do not meet at one or two corners) determine the percent of overlap as a function of the angle ABK and D.