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.

First, with the compass, make a circle with radius r. Then make 5 marks on the cirumference of the circle, so that if any two consecutive marks would have a line drawn from them to the center of the circle, they would form a 72 degree angle. Next connect the five marks on the circumference.

Posted by ethan on 2003-05-15 13:07:33