Suppose O (h, k) is the centre of the circle passing through the points P, Q and R.
∴ (h – 6)2 + (k + 6)2 = (h – 3)2 + (k + 7)2
∴ h2 – 12h + 36 + k2 + 12k + 36
= h2 – 6h + 9 + k2 + 14k + 49
∴ 6h + 2k = 14
∴ 3h + k = 7 …(i)[Dividing both sides by 2]
OP = OR …[Radii of the same circle]
∴ (h – 6)2 + (k + 6)2 = (h – 3)2 + (k – 3)2
∴ h2 – 12h + 36 + k2 + 12k + 36
= h2 – 6h + 9 + k2 – 6k + 9
∴ 6h – 18k = 54
∴ 3h – 9k = 27 …(ii)[Dividing both sides by 2]
Subtracting equation (ii) from (i), we get
Substituting the value of k in equation (i), we get
3h – 2 = 7
∴ 3h = 9
∴ h = 9/3 = 3
∴ The co-ordinates of the centre of the circle are (3, -2).
