Explanation

(d)
Given equation of circle is
$x^{2} + y^{2} - 2x - 4y - 20 = 0$
[image:11_image5.emf]
$\therefore$ centre is (1, 2) and
Radius, $r = \sqrt{1^{2} + 2^{2} + 20} = 5$
Now, $PC = \sqrt{(16 - 1)^{2} + (7 - 2)^{2}} = \sqrt{250}$
In $\mathrm{\Delta}PC\mathcal{Q}$,
$P\mathcal{Q} = \sqrt{PC^{2} - \mathcal{Q}C^{2}}$
$= \sqrt{\left( \sqrt{250} \right)^{2} - (5)^{2}} = 15$
$\therefore$ area of quadrilateral $P\mathcal{Q}CR$
$= 2\ area\ of\ \mathrm{\Delta}PC\mathcal{Q}$
$= \frac{2.1}{2}P\mathcal{Q}.\mathcal{Q}C$
$= 1.15.5 = 75$ sq unit