Circle Math

https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/
equation of circle: x^2 + y^2 + 2*g*x + 2*f*y + c = 0

2f = ( ( x1² – x3² )( x1 – x2 ) +( y1² – y3² )( x1 – x2 ) + ( x2² – x1² )( x1 – x3 ) + ( y2² – y1² )( x1 – x3 ) ) / ( y3 – y1 )( x1 – x2 ) – ( y2 – y1 )( x1 – x3 )

2g = ( ( x1² – x3² )( y1 – x2 ) +( y1² – y3² )( y1 – y2 ) + ( x2² – x1² )( y1 – y3) + ( y2² – y1² )( y1 – y3 ) ) / ( x3 -x1 )( y1 – y2 ) – ( x2 – x1 )( y1 – y3 )

c = -x1² – y1² – 2gx1 – 2fy1
center: (h = -g, k = -f)
radius: r^2 = h^2 + k^2 - c

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