Question

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?

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is 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 =${\left(\frac{4.8}{\sqrt{2}}\right)}^2$;

Area of circle: $\pi$ (2.4)${}^2$;

Area of the shaded region: $\frac{1}{2}$$\left(\pi \right(2.4{)}^2-{\left(\frac{4.8}{\sqrt{2}}\right)}^2)=\frac{(\pi -2){\left(\frac{12}{5}\right)}^2}{2}$