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 » Math Topics » geometry.pre-college.independent

Topic: Intersection
Replies: 1   Last Post: Aug 9, 2006 1:22 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Rich Kleinschmidt

Posts: 31
Registered: 12/6/04
Re: Intersection
Posted: Aug 9, 2006 1:22 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Your approach looks good. The algebra will be nothing that is beyond 2nd year algebra - just much uglier than any 2nd year text would ask you to tackle.

For example your 1st equation you get (y - b)^2 = Rab^2 - (x - a)^2
Then take the square root of both sides and get y = b +/- sqrt(Rab^2 - (x - a)^2)

Once you solve both equations for y, substitute for y and you get an equation two ugly radicals but only x. You can eliminate the radicals by isolating one and squaring both sides. Then isolating the other and squaring both sides.

You will need to keep track of the +/- ambiguities and possible extraneous solutions introduced by squaring. All the techniques are in 2nd year algebra.

Rich Kleinschmidt


-------------- Original message ----------------------
From: "Carlo Casini" <carlo_casini@worldnet.att.net>
> Hello,
> I need help on solving this problem.
> How do you find the intersection(s) of 2 circumferences knowing only the
> center and the radius of each one?
> I have look on several book and on the internet without any success.
> The only way that come to my mind is to represent the circumferences with a
> system of equation:
> (x - a)^2 + (y - b)^2 = Rab^2
> (x - c)^2 + (y - d)^2 = Rcd^2
> where a,b,c and d are the coordinate of the centers and Rab and Rcd the
> radiuses;
> I think x and y values should be the coordinate of the intersection(s)
> point(s).
> Any help would be greatly appreciated.



------- End of Forwarded Message



Date Subject Author
8/8/06
Read Intersection
Carlo Casini
8/9/06
Read Re: Intersection
Rich Kleinschmidt

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.