SOLUTION: please help Circumscribed about the triangle with vertices (2,3) (0,5) and (1,-1)

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Question 939843: please help Circumscribed about the triangle with vertices (2,3) (0,5) and (1,-1)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is the same as solving for the equation of a circle given three points.
Assume,
x%5E2%2By%5E2%2B2fx%2B2gy%2Bh=0
is the equation of the circle.
Inputting all three points gives,
4%2B9%2B4f%2B6g%2Bh=0
4f%2B6g%2Bh=-13
.
.
25%2B10g%2Bh=0
10g%2Bh=-25
.
.
1%2B1%2B2f-2g%2Bh=0
2f-2g%2Bh=-2
.
.
Solving these three simultaneous equations gives,
f=13%2F10
g=-17%2F10
h=-8
Then the circle becomes,
x%5E2%2By%5E2%2B%2813%2F5%29x-%2817%2F5%29y-8=0
Now complete the square,

%28x%2B13%2F10%29%5E2%2B%28y%5E2-17%2F5%29%5E2=1258%2F100
%28x%2B13%2F10%29%5E2%2B%28y%5E2-17%2F5%29%5E2=629%2F50
Center (-13%2F10,17%2F5)
Radius : sqrt%28629%2F50%29=sqrt%281258%29%2F10