Explanation

(b)
$\because$ Radius of circle =perpendicular distance of tangent $x + y - 5 = 0$ from the centre (1, 2)
$\therefore r = \frac{|1 + 2 - 5|}{\sqrt{1 + 1}} = \sqrt{2}$
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Hence, the required equation of the circle is
$(x - 1)^{2} + (y - 2)^{2} = \left( \sqrt{2} \right)^{2}$
$\Rightarrow x^{2} + 1 - 2x + y^{2} + 4 - 4y = 2$
$\Rightarrow x^{2} + y^{2} - 2x - 4y + 3 = 0$