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Circles Abound (2) (Posted on 2004-10-17) Difficulty: 4 of 5
I've a black circle of radius 5.

I wish to create 5 identical white circles of some lesser radius, which I will place on top of the black circle and completely obscure (cover) the black circle.

What is the smallest radius which I can make the smaller circles and still meet my requirement?

No Solution Yet Submitted by SilverKnight    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: a start | Comment 2 of 11 |
(In reply to a start by Charlie)

As this is a difficuty level 4 problem, the nice pentagon configuration would seem too easy, and it is! The problem is mentioned in Rouse Ball pp. 97-99 (no spoiler, really) and the radius ratio of .609383:1 is given as optimal whereas the pentagon approach gives .618034:1. The problem is evidently an old one as a solution was published by Neville in 1915. As some people get very upset by Google searches, I won't at this time say what I found using Google. 
  Posted by Richard on 2004-10-17 17:42:08

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