The equations of four circles are $(x \pm a)^{2} + (y \pm a)^{2} = a^{2}$ . The radius of a circle touching all four circles is

(2 - \sqrt{2}) a

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2 \sqrt{2} a

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(\sqrt{2} - 1) a

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(2 + \sqrt{2}) a

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Solution

The correct option is B $(\sqrt{2} - 1) a$
$d = \sqrt{(a + a)^{2} (a + a)^{2}}$
$= \sqrt{8 a^{2}}$
$= 2 \sqrt{2} a$
$2 \sqrt{2} a = 2 a + 2 r$
$r = (\sqrt{2} - 1) a$

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