The equations of four circles are (x±a)2+(y±a)2=a2 The radius of a circle touching all the four circles is

The four circle are as shown in the figure.The smallest circle touching all of them has radius 2a-aand the greatest circle touching all of them has radius 2a+a

The equations of four circles are (x±a)2+(y±a)2=a2 The radius of a circle touching all the four circles is

The four circle are as shown in the figure.The smallest circle touching all of them has radius 2a-aand the greatest circle touching all of them has radius 2a+a

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

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$(\sqrt{2} + 2) a$

$2 \sqrt{2} a$

$(\sqrt{2} + 1) a$

$(2 + \sqrt{2}) a$

answer is C.

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Detailed Solution

The four circle are as shown in the figure.
The smallest circle touching all of them has radius $\sqrt{2 a} - a$
and the greatest circle touching all of them has radius $\sqrt{2 a} + a$

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