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In the figure above point O is the center of the larger cir
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20 Aug 2020, 10:36
20 Aug 2020, 10:36
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GRE In the figure above point O is the center of the larger.png [ 11.14 KiB | Viewed 1662 times ]
In the figure above point O is the center of the larger circle and the two circles are tangent at point P. The line segment OP (not shown) is a diameter of the smaller circle. The area of the larger circle is what multiple of the area of the smaller circle?
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4
Re: In the figure above point O is the center of the larger cir
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20 Aug 2020, 13:24
20 Aug 2020, 13:24
1
So we have the area of the small circle is
\(A_{Small} = \pi * (\frac{OP}{2})^2 = \pi * \frac{OP^2}{4}\)
Then \(A_{Big} = \pi * OP^2.\)
We want \(\frac{A_{big} }{ A_{small}} = \pi * \frac{OP^2 }{ \pi * (OP^2/4)} = 4.\)
\(A_{Small} = \pi * (\frac{OP}{2})^2 = \pi * \frac{OP^2}{4}\)
Then \(A_{Big} = \pi * OP^2.\)
We want \(\frac{A_{big} }{ A_{small}} = \pi * \frac{OP^2 }{ \pi * (OP^2/4)} = 4.\)
gmatclubot
Re: In the figure above point O is the center of the larger cir [#permalink]
20 Aug 2020, 13:24
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