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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circles in a rectangle - difficult problem!
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bhumika.k.shah
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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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thephoenix
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bhumika.k.shah
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thephoenix
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IMO Abhumika.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
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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sanju09
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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: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
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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Sanjeev K Saxena
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