SOLUTION: What is the coordinate of the center of the circle circumscribing a triangle with endpoints at A(5,8), B(-1,0) and C(2,-4)?

Question 641598: What is the coordinate of the center of the circle circumscribing a triangle with endpoints at A(5,8), B(-1,0) and C(2,-4)?
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
let O,the center be (x,y)which is equidistant from the vertices of the triangle ABC
so (x-5)^2+(y-8)^2= (x+1)^2+(y-0)^2 i.e OA=OB
& (x-5)^2+(y-8)^2= (x-2)^2+(y+4)^2 i.e OA=OC
or by simplifying the above eqns
x^2+25-10x+y^2+64-16y=x^2+1+2x+y^2
or 12x+16y=88
or 3x+4y=22 ---------1
& x^2+25-10x+y^2+64-16y=x^2+4-8x+y^2+16+8y
or 2x+24y=69 ---------2
by solving 1 & 2
x=63/16 & y=489/168
ans

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