Show, how given a distance r, one can construct a regular pentagon, whose circumradius is r, using only ruler and compass...

Note 1: The ruler doesn't have any marks, so it's no good for measuring. It's only good for joining 2 points by a line.

Note 2: The circle which circumscribes the polygon, such that the polygon lies entirely within the circle and all of whose vertices lie on the circumference of the circle is the circumcircle of the polygon. The radius of this circle is the circumradius of the circle.

(In reply to re(2): Solution by Ravi Raja)

Ravi, perhaps you are missing the point. With nothing but a compass for drawing circles and a straight edge for drawing lines, one can easily make a ninety or sixty degree angle and bisect them ad infinitum. But how does one create an angle of 72 degrees (or any angle that is not a multiple of 15, for that matter)? Only when you answer that will you fully answer the original question.

Posted by Bryan on 2003-05-16 06:37:20