Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).

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Solution

Let the circumcentre be O(x,y)
Circumcentre is equidistant from the vertices.
OA= OB = OC

OA =
OB = $\sqrt{(x + 1)^{2} + y^{2}}$
OC =

OA = OB
OA=OB

x + 3y + 6 = 0 ----- (i)

OB=OC
OB=OC
=

4x-3y-21 =0 ----- (ii)

Add i and ii
5x-15=0
x=3
y=-3
Circumcentre is (3,-3)

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