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

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Q. 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

KEAMKEAM 2015Straight Lines

Solution:

In a right angle triangle, the mid-point of the hypotenuse is the circumcentre
image
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 $(0,4)$.