Coordinates of points on a circle are A (3, 0), B(-1, -6) and C(4,-1)

Let the coordinates of the centre of the circle be O(x, y)

Using distance formula =

Since the distance of the points A, B and C will be equal from the center, therefore

⇒ OA = OC

On squaring both sides, we get

=

⇒ x² + 9 - 6x + y² = x² + 2x +1 + y² + 36 + 12y

⇒ -8x - 12y = 28

⇒ 2x + 3y = -7------------- (1)

Similarly, OC = OB

On squaring both sides, we get

=

⇒ x² + 16 - 8x + y² + 1 + 2y = x² + 1 +2x + y² + 36 + 12y

⇒ -10x - 10y = 20

⇒ x + y = -2 ------------- (2)

Solving eqn (1) and (2), we get

x = 1; y = -3

Coordinates of circum center are (1, -3)

Circum radius of the circle = OA =

=

= units