Question

A semicircle is drawn with $AB$ as its diameter. From $C$ a point on $AB$ a line perpendicular to $AB$ is drawn meeting the circumference of the semicircle at $D$. Given that $AC=2cm$ and $CD=6cm$ the area of the semicircle is :

• A. $32\pi$
• B. $50\pi$
• C. $40\pi$
• D. $36\pi$

Answer 1

The correct option is B $50\pi$

Let O be the centre of the circle. Then, $OA=OB=OD=r$
Now, $OC=r-2$
and $CD=6$
Thus, in $△ODC$
$O{C}^2+C{D}^2=O{D}^2$
$(r-2{)}^2+6^2=r^2$
$r^2+4-4r+36=r^2$
$4r=40$
$r=10$ $cm$
Area of semicircle $=\frac{\pi r^2}{2}=\frac{\pi (10{)}^2}{2}=50\pi$