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Tough Isosceles (Posted on 2005-07-20) Difficulty: 3 of 5
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?

See The Solution Submitted by McWorter    
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Hints/Tips Playing around with Geometer's Sketchpad.... | Comment 1 of 6
... it looks as if, when the condition is met, arc AD is half of arc BD, and therefore 1/3 of arc AB.  If this is actually the case (I haven't proven), then accomplishing this would provide a way of trisecting angle BOA.  But that's impossible with compass and straightedge.

Edited on July 20, 2005, 3:53 pm
  Posted by Charlie on 2005-07-20 15:50:33

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