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 = 2 cm and CD
= 6 cm, the area of the semicircle (in sq. cm) will be:
a) 50π
b) 55π
c) 31π
d) 82π; 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 = 2 cm and CD; = 6 cm, the area of the semicircle (in sq. cm) will be:; a) 50π; b) 55π; c) 31π; d) 82π

Answer 1

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=[π(x)^2]/2
area=50π

$<b>hope it helps$ ❣️✌️