circles in a rectangle - difficult problem!

[bhumika.k.shah]

The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

[thephoenix]

pls mention the length of diag

[bhumika.k.shah]

Done!

pls mention the length of diag

[thephoenix]

The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

IMO A
pls mention the length of diag

let width of rect be x ; then length=2x

d=diag

d^2=x^2+(2x)^2
=5x^2

x=d/ ryt5=d(rut 5)/5

x/2=d(rut5)/10

area of circle=pie(x/2)^2
=pie* (d^2)5/100=d^2/20=(rut80)^2/20=4pie

[sanju09]

The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

The rectangle has its length twice of its width in here. So, if x cm is width, 2 x cm is the length; such that:

x^2 + (2 x) ^2 = 80

Or x = 4, same as the diameter of each circle in here; the area of each of the circles in here is therefore, [spoiler]4 π[/spoiler] square centimeter.

[spoiler]A[/spoiler]