# Question:Miquel Five Circle Theorem, fsolve

## Question:Miquel Five Circle Theorem, fsolve

Maple

I am interested in the 5 circle theorem of Miquel.  Search on the internet 'Miquel five circle theorem' for more details. I would like to prove this theorem using Maple, and also see if there is a generalisation to this for more than 5 circles.  I wish to find the points of intersection of the circles and am using the fsolve command:

fsolve({(x-x[i])^2+(y-y[i])^2-r[i]^2, (x-x[i-1])^2+(y-y[i-1])^2-r[i-1]^2}, {x, y});

I am using the curly braces for sets - as I can't seem to get it to work for [] lists.   The output gives something like {x=12.0005, y=4.65}.  I want to use these values to obtain straight line equations and verify that the lines formed by successive circles form a pentagram, with all vertices on the five circles.  I just want to get to the floating point values, without the x= part.  The type of the returned expressions is '=' - whatever that means!

I'm also wondering if using the plottools and plots packages is sufficient - as opposed to the geometry pakage.

I'm interested in how many people have heard of this theorem.  Does it have any generalisations to 6, 7, ... circles?

Any help or comments gratefully received.

David.

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