Yes, one more reason to be humble, I know. This is the simplest problem I couldn't solve so far. Assume we have a circle of center O, a ruler of arbitrary size and a pencil. We use the ruler and the pencil to choose 4 points on the circle - the extremities of two diametral/diagonal segments. They build a rectangle. So far so good. Using the ruler only and the pencil, how can I draw the segment ED (with E the intersection of a line passing through D and the prolongation of AB) which is parallel to the diagonal segment BC? Thank you for illuminating me.