Coordinates of points on a circle are A(6, -6), B(3, -7) and C(3, 3).
Let the coordinates of the centre of the circle be O(x, y)
Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Since the distance of the points A, B and C will be equal from the center, therefore
⇒ OA = OC
\(\sqrt{(x - 6)^2 + (y + 6)^2}\) = \(\sqrt{(x - 3)^2 + (y - 3)^2}\)
On squaring both sides, we get
(x - 6)2 + (y + 6)2 = (x - 3)2 + (y - 3)2
x2 - 12x + 36 + y2 + 12y + 36
= x2 - 6x + 9 + y2 - 6y + 9
x - 3y = 9........(1)
Similarly, OA = OB
\(\sqrt{(x - 6)^2 + (y + 6)^2}\) = \(\sqrt{(x - 3)^2 + (y + 7)^2}\)
On squaring both sides, we get
(x - 6)2 + (y + 6)2 = (x - 3)2 + (y + 7)2
x2 - 12x + 36 + y2 + 12y + 36
= x2 - 6x + 9 + y2 + 14y + 49
3x + y + 7.......(1)
Solving eqn (1) and (2), we get
x = 3; y = - 2
Coordinates of circum center are (3, - 2)