Find the centre of a circle passing through the points (6, - 6), (3, - 7) and (3, 3).
Given that circle passes through the points A(6, - 6), B(3, - 7), C(3, 3).
Let us assume O(x, y) be the centre of the circle.
We know that distance from the centre to any point on h circle is equal.
So, OA = OB = OC
We know that distance between two points (x1, y1) and (x2, y2) is 
Now,
⇒ OA = OB
⇒ OA2 = OB2
⇒ (x - 6)2 + (y - (- 6))2 = (x - 3)2 + (y - (- 7))2
⇒ (x - 6)2 + (y + 6)2 = (x - 3)2 + (y + 7)2
⇒ x2 - 12x + 36 + y2 + 12y + 36 = x2 - 6x + 9 + y2 + 14y + 49
⇒ 6x + 2y = 14
⇒ 3x + y = 7 ..... (1)
Now,
⇒ OB = OC
⇒ OB2 = OC2
⇒ (x - 3)2 + (y - (- 7))2 = (x - 3)2 + (y - 3)2
⇒ (x - 3)2 + (y + 7)2 = (x - 3)2 + (y - 3)2
⇒ x2 - 6x + 9 + y2 + 14y + 49 = x2 - 6x + 9 + y2 - 6y + 9
⇒ 20y = - 40
⇒ y = - 2 .... - (2)
Substituting (2) in (1), we get
⇒ x = 3
∴ (3, - 2) is the centre of the circle.
We know radius is the distance between the centre and any point on the circle.
Let ‘r’ be the radius of the circle.
⇒ r = √(9 + 16)
⇒ r = √25
⇒ r = 5
∴ The radius of the circle is 5.