Tough Geom2

[maihuna]

A semi- circle 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 semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm.) will be:

a) 32Ï€

b) 50Ï€

c) 40.5Ï€

d) 81Ï€
e) 162 II

[mruzeful]

is it A?

r=2+6

and area = (pi)r^2/2 = 32(pi)

[real2008]

it should be B

[aa2kash]

draw a line from the centre of the circle to the point D. this is equal to the radius of the circle.

Now u have a right angle traingle with the sides
6, r and r-2
solve it and get r=10.
area of semicircle is pi*r*r/2 = 50pi

[GMATQuantCoach]

Connect AD and BD.

Triangle ADB must be a right triangle.

We can show that triangle ACD is similar to triangle DCB. Then
AC/CD = CD/CB

CD^2 = AC * CB
36 = 2 * CB
CB = 18

Radius = (AC + CB)/2 = 10

Area of Semi-Circle = 1/2 * pi * r^2 = 50pi

B is the answer.