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Two circles o...

Question

Two circles of equal radius $r$ cut orthogonally. If their centres are $(- 2, - 3)$ and $(- 5, - 6)$ , then $r =$

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Solution

The correct option is C $3$
If two circles are orthogonal to each other , then
$r {_{1}}^{2} + r {_{2}}^{2} = (c_{1} c_{2})^{2}$
Given $r_{1} = r_{2} = r$ and $c_{1} = (- 2, - 3)$ and $c_{2} = (- 5, - 6)$
So, $2 r^{2} = (3 \sqrt{2})^{2}$
$r^{2} = 9$
$r = 3$

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