The equation of a circle is \( x^{2}+y^{2}=4 \). The centre of the smallest circle touching this...

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The equation of a circle is \( x^{2}+y^{2}=4 \). The centre of the smallest circle touching this circle and the line \( x+y=5 \sqrt{2} \) has the coordinates
(a) \( \left(\frac{7}{2 \sqrt{2}}, \frac{7}{2 \sqrt{2}}\right) \)
(b) \( \left(\frac{3}{2}, \frac{3}{2}\right) \)
(c) \( \left(-\frac{7}{2 \sqrt{2}},-\frac{7}{2 \sqrt{2}}\right) \)
(d) none of these
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