PQR is a right angled triangle with PQ=8, QR=6, QT as altitude. If a circle is d

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PQR is a right angled triangle with PQ=8, QR=6, QT as altitude. If a circle is drawn with QT as diameter, what is the area of the shaded region?

PQR Is A Right Angled Triangle With PQ=8, QR=6, QT As Altitu...

Answer: Option C
:
C
Let PT=x, Then 8

^{2}

-x

^{2}

= 6

^{2}

- (10-x)

^{2}

;

\Rightarrow

x = 6.4
Thus QT = 8

^{2}

- 6.4

^{2}

= 4.8; ST=

\frac{4.8}{\sqrt{2}}

;
Area of square STUQ =

{(\frac{4.8}{\sqrt{2}})}^{2}

;
Area of circle:

π

(2.4)

^{2}

;

PQR Is A Right Angled Triangle With PQ=8, QR=6, QT As Altitu...

Area of the shaded region:

\frac{1}{2}

(π (2.4)^{2} - {(\frac{4.8}{\sqrt{2}})}^{2}) = \frac{(π - 2) {(\frac{12}{5})}^{2}}{2}

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