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Points On A Circle II (Posted on 2010-07-13) Difficulty: 3 of 5
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: Thoughts on Part (B) | Comment 11 of 12 |
(In reply to Thoughts on Part (B) by Dej Mar)

Dej Mar:


Thanks for giving us a point of attack for part B.  I'm probably missing something, but I don't following your thinking. 

What do you mean by a rational angle?  Is this in degrees or radians, as they cannot both be rational?  And why do you think that the angle needs to be rational?

And for that matter, which problem are you trying to solve?  Part B seems to me to really be two parts, B1 and B2.  B1 allows any radius and B2 requires a rational radius.

It seems to me that for the simpler 3-point problem, B1 and B2 have different solutions, but I suspect that they have the same solution for the simpler 4 point problem.  

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