Find the equation of a circumcircle of a triangle whose testices are A (2, 3), B (5, 4) and C (3, 7)

Answer 1

that's vertices, not testices.

The circumcenter lies at the intersection of the sides' perpendicular bisectors.

So, to start, find the equations of two of the bisectors.

AB: slope=1/3 midpoint is (7/2,7/2)
pb: (y-7/2) = (-3)(x-7/2)

AC: slope=4 midpoint is (5/2,5)
pb: (y-5) = (-1/4)(x-5/2)

the pb intersect at D:(67/22,107/22)

The distance AD is √2210/22

So, the circle is

(x-67/22)^2 + (y-107/22)^2 = 2210/484

see the graphs at

http://www.wolframalpha.com/input/?i=plot+y-3+%3D+%281%2F3%29%28x-2%29%2C+y-3+%3D+%284%29%28x-2%29%2C+y-4+%3D+%28-3%2F2%29%28x-5%29%2C+%28x-67%2F22%29^2+%2B+%28y-107%2F22%29^2+%3D+2210%2F484

Answer 2

I need the working and answer