Question

The circumcentre of the triangle with vertices $(0,0),(3,0)$ and $(0,4)$ is

• A. $(1,1)$
• B. $(2,\frac{3}{2})$
• C. $(\frac{3}{2},2)$
• D. none of these

Answer 1

Answer: (C)

$(\frac{3}{2},2)$

Let $A(0,0),B(3,0)$ and $C(0,4)$ be the coordinates
and coordinates of circumcentre be $O(h,k)$
Then $OA=OB=OC$
$\Rightarrow {\left(OA\right)}^2={\left(OB\right)}^2={\left(OC\right)}^2\Rightarrow {(h-0)}^2+{(k-0)}^2={(3-h)}^2+{(0-k)}^2={(0-h)}^2+{(4-k)}^2$
Solving this we get
$h=\frac{3}{2},k=2$