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August 21, 2014

August 21, 2014

Posted by **Sally** on Thursday, July 2, 2009 at 6:01pm.

- Math -
**MathMate**, Thursday, July 2, 2009 at 6:35pmBy inspection, the centre of the circle is at (8,8), since the three given points form a right-triangle in which the hypothenus is the diameter (0,8),(16,8).

The radius is half the diameter, namely (16-0)/2=8

The standard form of a circle with centre at (xo,yo) and radius of R is

(x/xo)^{2}+ (y/yo)^{2}= R^{2}

Can you take it from here?

Note:

If you are looking for the general case of a circle passing through three distinct points P1(x1,y1), P2(x2,y2) and P3(x3,y3), it can be obtained by evaluating the following 4x4 determinant:

x^{2}+ y^{2}x y 1

x1^{2}+ y1sup>2 x1 y1 1

x2^{2}+ y2sup>2 x2 y2 1

x3^{2}+ y3sup>2 x3 y3 1

- Math -
**MathMate**, Thursday, July 2, 2009 at 6:37pmSorry, the determinant does not show up very well, and there was a typo:

x^{2}+ y^{2}x y 1

x1^{2}+ y1^{2}x1 y1 1

x2^{2}+ y2^{2}x2 y2 1

x3^{2}+ y3^{2}x3 y3 1

- Math -
**MathMate**, Thursday, July 2, 2009 at 9:42pmPlease ignore the following format testing:

<pre>

x^{2}+ y^{2}x1 y1 1

x1^{2}+y1^{2}x1 y1 1

x2^{2}+y2^{2}x2 y2 1

x3^{2}+y3^{2}x3 y3 1

</pre>

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