Question

The circumcentre of the triangle whose vertices are $(-2,-3),(-1,0),(7,-6)$ is

• A. $(-3,3)$
• B. $(3,-3)$
• C. $(-3,-3)$
• D. None of these

Answer 1

Answer: (B)

$(3,-3)$

The vertices of the triangle are
$P\equiv (-2,-3),Q\equiv (-1,0),R\equiv (7,-6)$
Let $A(x,y)$ be the circumcentre of $△PQR$
Therefore, ${AP}^2={AQ}^2$
$\Rightarrow {(x+2)}^2+{(y+3)}^2={(x+1)}^2+y^2$
$\Rightarrow 4x+6y+13=2x+1$
$\Rightarrow 2x+6y+12=0$
$\Rightarrow x+3y=-6$ ...(i)

Similarly ${AP}^2={AR}^2$
$\Rightarrow {(x+2)}^2+{(y+3)}^2={(x-7)}^2+{(y+6)}^2$
$\Rightarrow 3x-y=12$ ....(ii)
From Eqs(i) and (ii), we get
$(x,y)\equiv (3,-3)$
Here, circumcentre is $(3,-3)$.