Let A and B be different points on a circle with center O. With only a straightedge and a compass, can you construct a straight line through O meeting the segment AB at C, C strictly between A and B, and meeting the circle at D, so that C is between O and D and the segments AC and AD have the same length?

My previous comment works under the assumption that C is required to be the midpoint of AB. However, re-reading the problem, I see the word Strictly, not Exactly, between A and B. If that changes the meaning of the problem, my thoughts were probably wrong. In any case, any arc with center A, if it crosses the circle at D and line AB at C will make AD equal to AC, but C, D, and O will not necessarily be colinear.

Posted by Bret on 2005-07-20 17:31:21