Find the centre of a circle passing through the points (6, -6), (3, -7) and (3,3).Also find the radius.                                                                                                                                      (Ans: (3, -2), 5 units)

Ans:    OA=OB = OC = radius of the circle where O is the centre of the circle and let O be (x, y)

OA² = OB² = OC²

OA² = (x-6)² + (y+6)² = x² + y² - 12x + 36 + 12y + 36

OB² = (x-3)² + (y+7)² = x² + y² - 6x + 9 + 14y + 49

OC² = (x-3)² + (y-3)² = x² + y² - 6x + 9 - 6y + 9

OA² = OB²

x² + y² - 12x + 12y + 72 = x² + y² - 6x + 14y + 58

- 12x + 12y + 6x - 14y + 72 - 58 = 0

- 6x - 2y + 14 = 0

- 3x - y + 7 = 0           ...............(1)

x² + y² - 6x + 9 + 14y + 49 = x² + y² - 6x + 9 - 6y + 9

- 6x + 14y + 58 = -6x - 6y + 18

14y + 6y = 18 - 58

20y = - 40

y = - 2                          ...............(2) Substituting we get

- 3x + 2 + 7 = 0

- 3x = - 9 x = 3

(x, y) = (3, -2)

Diameter = 3² + 2² - 6(3) + 18 - 6 (-2)

= 9 + 4 - 18 + 18 + 12

= 13 + 12 = 25

Radius =   √ 25 = 5 units