Segment QR of length r is a tangent at Q to a circle of radius r with centre at P What is the area o...........

Quantitative Aptitude (CDS) Mensuration 2D

Segment QR of length r is a tangent at Q to a circle of radius r with centre at P. What is the area of the part of the triangle PQR, which is outside the circular region?

$\frac{\pi r^{2}}{16}$

$\frac{r^{2}}{2}- \frac{\pi r^{2}}{8}$

$\frac{r^{2}}{2}- \frac{\pi r^{2}}{16}$

$\frac{r^{2}}{4}- \frac{\pi r^{2}}{8}$

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Explanation:

As, PQR is a triangle and QR = r
Radius of circle = r
Area of shaded region = area of triangle PQR – area of sector PQSP
$=> Area \: of \: shaded\: region = \frac{1}{2}r^{2}-\frac{45^{o}}{360^{o}}\times\pi r^{2}=\frac{r^{2}}{2}-\frac{\pi r^{2}}{8}$
Hence option(2)