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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)

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 Thoughts on Part (B) | Comment 10 of 12 |

The original post is altered, as it was a bit off-base and I am far from an expert in this area.

I know there are tests that can help determine whether a number may be rational, but those I found do not seem to be  simple tests.  As this problem was rated only 3 of 5, I would think there must be a simple test I am unaware of. How to find a heptagon (regular or irregular) with integer sides that can be inscribed inside a circle with a rational radius with my limited knowledge seems to be difficult.

Edited on July 16, 2010, 8:24 pm
 Posted by Dej Mar on 2010-07-16 08:15:00

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