The Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » Math Topics » geometry.puzzles

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Three Points and a Circle
Replies: 3   Last Post: Mar 1, 2012 11:18 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bret Jolly

Posts: 13
Registered: 12/6/04
Re: Three Points and a Circle
Posted: Aug 2, 1993 11:14 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

The question is how to calculate the Cartesian equation
of a circle given the coordinates of three of its points.

Let the points be (x1,y1), (x2,y2), and (x3,y3). Then
the circle is given by

/ \
| 1 x y x^2 + y^2 |
det | 1 x1 y1 x1^2 + y1^2 | = 0
| 1 x2 y2 x2^2 + y2^2 |
| 1 x3 y3 x3^2 + y3^2 |
\ /

This equation is clearly a circle from its form, and
it passes through each of the three points because when
(x,y) equals one of those points, two rows of the determinant
will be the same.

Similar techniques can be used for many other figures.

Regards, Bret

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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.