Question 940005
<pre> 
This involves solving a 3x3 system of equations,
either by substitution or elimination, Cramer's rule,
Gaussian elimination, Gauss-Jordan method, or the 
inverse matrix method, whichever method you have
studied.

{{{drawing(200,200,-6,4,-3,7,graph(200,200,-6,4,-3,7),
triangle(2,3,0,5,1,-1),
circle(-1.3,1.7,3.54682957),locate(.1,5.5,"(0,5)"),
locate(2.1,3.1,"(2,3)"),locate(1,-1,"(1,-1)"),

circle(0,5,0.15),circle(0,5,0.13),circle(0,5,0.11),circle(0,5,0.09),circle(0,5,0.07),circle(0,5,0.05),circle(0,5,0.03),circle(0,5,0.01),

circle(2,3,0.15),circle(2,3,0.13),circle(2,3,0.11),circle(2,3,0.09),circle(2,3,0.07),circle(2,3,0.05),circle(2,3,0.03),circle(2,3,0.01),

circle(1,-1,0.15),circle(1,-1,0.13),circle(1,-1,0.11),circle(1,-1,0.09),circle(1,-1,0.07),circle(1,-1,0.05),circle(1,-1,0.03),circle(1,-1,0.01)

  )}}}

Those three points are on the circle so they will satisfy
the equation:

{{{x^2+y^2+Dx+Ey+F=0}}}

Substituting the three vertices gives this system:

{{{system(2^2+3^2+D(2)+E(3)+F=0,0^2+5^2+D(0)+E(5)+F=0,1^2+(-1)^2+D(1)+E(-1)+F=0)}}} 

which simplifies to:

{{{system(2D+3E+F=-13,5E+F=-25,D-E+F=-2)}}}

Solve that system for D, E, and F and substitute in

{{{x^2+y^2+Dx+Ey+F=0}}}

You solve that.  Hint: one of those three values is -3.4,
but I won't tell you whether it is D, E, or F.  :)

Edwin</pre>