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        riddles >> hard >> A Cubic And Inscribed Problem?
        
(Message started by: K Sengupta on Feb 4^th, 2006, 11:39pm)

Title: A Cubic And Inscribed Problem?
Post by K Sengupta on Feb 4^th, 2006, 11:39pm

I am looking for a solution to the undernoted problem.

PROBLEM:

A hexagon is inscribed in a circle with radius r. Two of it's sides have length 2 and the last two have length 3.

Prove that r is a root of the equation:
2r³- 7r- 3= 0 .

Title: Re: A Cubic And Inscribed Problem?
Post by Barukh on Feb 5^th, 2006, 4:17am

I don't think the data given is sufficient to deduce the required answer.

Title: Re: A Cubic And Inscribed Problem?
Post by Sjoerd Job Postmus on Feb 5^th, 2006, 7:46am

on 02/04/06 at 23:39:59, K Sengupta wrote:

Let's imagine, just for the fun of it... that the other two sides are 300 and 301, for the fun of it. This'd give an answer. But, what if the two sides are 400 and 401, that'd give a totally different answer!

So, I must say, I can not solve it... too many ungivens. (not enough givens)

Title: Re: A Cubic And Inscribed Problem?
Post by towr on Feb 5^th, 2006, 7:50am

I think he forgot a few sides..

Title: Re: A Cubic And Inscribed Problem?
Post by pex on Feb 5^th, 2006, 1:47pm

It does seem to work if both other sides have length 1.