Question

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also , find its circumradius.

Answer 1

A(3,0)
B(-1,-6)
C(4,-1)

Let the circumcentre be O(x,y)
Circumcentre is equidistant from A, B and C.
Hence, OA = OB = OC
OA =
OB =
OC = ------- (iii)

From i and ii

---------(iv)

From (i) and iii

=


from (iv) and 2 (v)
2x+3y+7=0
-2x+2y +8 =0
___________
5y+15=0

y = -3

x = 1

So the circumcenter is (1,-3).
Circumradius =