Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: circle intersections...
Replies: 26   Last Post: Sep 1, 2013 10:49 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Chris M. Thomasson

Posts: 162
Registered: 8/29/13
Re: circle intersections...
Posted: Aug 30, 2013 3:50 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> "Ken Pledger" wrote in message
> news:ken.pledger-BBFD52.16002730082013@news.eternal-september.org...


> In article <kvok88$gf8$1@speranza.aioe.org>,
> "Chris M. Thomasson" <no@spam.invalid> wrote:


> > [cross-posted to {alt.math, sci.math}]
> >
> > "Chris M. Thomasson" wrote in message
> > news:kvoe76$155$2@speranza.aioe.org...
> >
> > I was wondering where I could find some programming
> > methods of clever circle intersection algorithms that use
> > a single square root operation....


> Your code is hard to read, but here's a standard trick to do what you
> want. Consider the circles


> x^2 + y^2 + 2x - 4y - 4 = 0

> x^2 + y^2 - 6x + 2y + 6 = 0.

> Subtract one equation from the other to get

> 8x - 6y - 10 = 0.

[...]

I came up with the following equations from your example:

((3y+5) / 4)^2 + y^2 + 2((3y + 5) / 4) - 4y - 4 = 0

x^2 + ((4x - 5) / 3)^2 + 2x - 4((4x - 5)/3) - 4 = 0


Which does indeed mean that:

x = 1.4
y = 0.2


Which is the same answer you got here:

> The circles in my example actually touch, so the line is their common
> tangent. The same solution method finds their point of contact (7/5,
> 1/5).



Okay, now I am getting somewhere. Thanks again Ken!

:^)




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.