Let A(3, 0), B(-1, -6) and C(4 , -1) be the given points.
Let O(x , y) be the circumcenter of the triangle
Then, OA = OB = OC
OA2 = OB2
(x – 3)2 + (y – 0)2 = (x + 1)2 + (y + 6)2
x2 + 9 – 6x + y2 = x2 + 1 + 2x + y2 + 36 + 12y
-8x -12y = 28
2x + 3y = -7 …..(i) [After simplification]
Again,
OB2 = OC2
(x + 1)2 + (y + 6)2 = (x – 4)2 + (y + 1)2
x2 + 2x + 1 + y2 + 36 + 12y = x2 + 16 – 8x + y2 + 1 + 2y
10x + 10y = -20
x + y = -2 …..(ii) [After simplification]
Hence, the circumcenter of the triangle is (1, -3)
Circumradius = distance from any of the given points (say B)
=√[(1 + 1)2 + (-3 + 6)2]
= √(4 + 9)
= √13 units