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# In the figure above, point O lies at the center of both circles. If th

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In the figure above, point O lies at the center of both circles. If th  [#permalink]

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24 Mar 2020, 07:58
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96% (00:59) correct 4% (01:14) wrong based on 25 sessions

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In the figure above, point O lies at the center of both circles. If the length of OP is 6 and the length of PQ is 2, what is the ratio of the area of the smaller circle to the area of the larger circle?

(A) 3/8

(B) 7/16

(C) 1/2

(D) 9/16

(E) 5/8

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Re: In the figure above, point O lies at the center of both circles. If th  [#permalink]

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26 Mar 2020, 10:15
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Solution

Given
In this question, we are given that
• In the given figure, point O lies at the center of both circles.
• The length of OP is 6 and the length of PQ is 2

To find
We need to determine
• The ratio of the area of the smaller circle to the area of the larger circle

Approach and Working out
As OP = 6, the radius of the smaller circle = 6
• Hence, area of the smaller circle = $$π6^2= 36π$$

As PQ = 2, the radius of the larger circle = 6 + 2 = 8
• Hence, area of the larger circle = $$π8^2 = 64π$$

Therefore, the required ratio = $$\frac{36π}{64π} = \frac{9}{16}$$

Thus, option D is the correct answer.

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Re: In the figure above, point O lies at the center of both circles. If th  [#permalink]

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29 Mar 2020, 04:04
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Attachment:
5674.jpg

In the figure above, point O lies at the center of both circles. If the length of OP is 6 and the length of PQ is 2, what is the ratio of the area of the smaller circle to the area of the larger circle?

(A) 3/8

(B) 7/16

(C) 1/2

(D) 9/16

(E) 5/8

The area of the smaller circle is π x 6^2 = 36π. The area of the larger circle is π x (6 + 2)^2 = 64π. The ratio of the smaller circle to the larger circle is 36π/64π = 36/64 = 9/16.

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Re: In the figure above, point O lies at the center of both circles. If th   [#permalink] 29 Mar 2020, 04:04