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circles in a rectangle - difficult problem!

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by bhumika.k.shah » Sat Jan 30, 2010 12:06 am
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
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Last edited by bhumika.k.shah on Sat Jan 30, 2010 12:24 am, edited 1 time in total.
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by thephoenix » Sat Jan 30, 2010 12:20 am
pls mention the length of diag
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by bhumika.k.shah » Sat Jan 30, 2010 12:29 am
Done! :-P
thephoenix wrote:pls mention the length of diag
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by thephoenix » Sat Jan 30, 2010 12:32 am
bhumika.k.shah wrote: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
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by sanju09 » Sat Jan 30, 2010 3:16 am
bhumika.k.shah wrote: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]
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