Let A (-3, 1), B (0, -2) and C (1, 3) be the vertices of the triangle.
Suppose O (h, k) is the circumcentre of ∆ABC.
∴ (h + 3)2 + (k – 1)2 = h2 + (k + 2)2
∴ h2 + 6h + 9 + k2 – 2k + 1 = h2 + k2 + 4k + 4
∴ 6h – 2k + 10 = 4k + 4
∴ 6h – 2k – 4k = 4 – 10
∴ 6h – 6k = – 6
∴ h – k = -1 ,..(i)[Dividing both sides by 6]
OB = OC …[Radii of the same circle]
∴ h2 + (k + 2)2 = (h – 1)2 + (k – 3)2
∴ h2 + k2 + 4k + 4 = h2 – 2h + 1 + k2 – 6k + 9
∴ 4k + 4 = -2h + 1 – 6k + 9
∴ 2h+ 10k = 6
∴ h + 5k = 3 …(ii) Subtracting equation (ii) from (i), we get
Substituting the value of k in equation (i), we get
h - 2/3 = -1
∴ h = -1 + 2/3
∴ h = -1/3
∴ The co-ordinates of the circumcentre of the triangle are (-1/3, 2/3)
