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 in square cm will be ?	Choose the most appropriate option.
A) 30pi
B) 40pi
C) 50pi
D) 60pi
E) 70pi
let O be center of circle and radius be x.   C can be anywhere on AB.Let us suppose that C is somewhere between A and O.   AC=2cm....so CO=(x-2)   DO=x,CD=6cm   CDO form a right angled triangle with right angle at C.   Using Pythagoras theorem,   x^2=6^2+(x-2)^2   4x=40   x=10cm   area=[pi(x)^2]/2   area=50pi   ANSWER:50pi
<result>C</result>
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 in square cm will be ?