Find the coordinates of the centre of the circle passing through A(5,1), B(-3,-7) and C(7,-1).

Find the coordinates of the centre of the circle passing through A(5,1), B(-3,-7) and C(7,-1).

let the coordinates of the centre be O(h,k).

the distance from the centre to a point on the circumference is equal to radius.

therefore OA=OB=OC

now from distance formula

now taking

now solving equation (1) and (2),

multiply (1) by 3 and subtract from (2)

substitute the value of h in (1)

hence the coordinates of the centre is (2,-4).

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