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Points $A(-1, y)$ and $B(5, 7)$ lie on a circle with centre $O(2, -3y)$ such that $AB$ is a diameter of the circle. Find the value of $y$. Also, find the radius of the circle.
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Centre $O (2, -3y)$ is the mid point of $AB$
$\frac{-1+5}{2} = 2$, $\frac{y+7}{2} = -3y$
$\Rightarrow y = -1$
Radius = $OB = \sqrt{(5 - 2)^2 + (7 - (-1))^2} = 5$
$\frac{-1+5}{2} = 2$, $\frac{y+7}{2} = -3y$
$\Rightarrow y = -1$
Radius = $OB = \sqrt{(5 - 2)^2 + (7 - (-1))^2} = 5$