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 Points On A Circle II (Posted on 2010-07-13)
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.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Thoughts on Part (B) Comment 12 of 12 |
(In reply to re: Thoughts on Part (B) by Steve Herman)

You can ignore my thoughts on Part (B). Looking into it further, I believe I was off-track.

Part B.1:
Intuitively, the smallest radius of the circle would be where a regular heptagon with side length 1 was inscribed. The length from the midpoint of one side to the center of this heptagon would be 2*COS(1/7 pi) =~ 1.801938. The radius of the circle would then be SQRT([2*COS(1/7 pi)]2+1/4) =~ 1.870021.
This would satisfy the conditon for any two adjacent points, but not for any two points.

Edited on July 17, 2010, 9:28 am
 Posted by Dej Mar on 2010-07-16 19:41:44

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