Question

Let $A\left(0,0\right)$ and $B\left(8,0\right)$ be two vertices of a right angled triangle whose hypotenuse is $BC.$ If the circumcentre is $(4,2)$, then the point $C$ is

• A. (2, 4)
• B. (0, 8)
• C. (0, 4)
• D. (0, 6)
• E. (2, 8)

Answer 1

Answer: (C)

In a right angle triangle, the mid-point of the hypotenuse is the circumcentre

Let the coordinates of the point $C$ be $(x,y)$.
Then, $\left(\frac{8+x}{2},\frac{0+y}{2}\right)=(4,2)$
$\Rightarrow \frac{8+x}{2}=4$ and $\frac{0+y}{2}=2$
$\Rightarrow x=0$ and $y=4$
Hence, coordinates of $C$ are $(0,4)$.