Refer to Points On A Circle.

(A) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured along the circumference, is an integer.

What is the smallest radius of the circle, given that each of the distances is unique?

(B) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured as a straight line, is an integer.

Determine the smallest radius of the circle. What is the smallest radius of the circle, given that it is rational?

Note: In Part (B) each of the distances may or may not be unique.

(In reply to re(3): Part A - a further reduction by Dej Mar)

I vote with Harry.  (Great work, by the way).  If there is only one pair of points that are 24 units apart, then the problem condition is satisfied, even if that 24 unit distance can be obtained in two different ways.  

Posted by Steve Herman on 2010-07-16 02:49:45