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# If the two circles shown above are concentric with center O, which exp

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Math Expert
Joined: 02 Sep 2009
Posts: 53831
If the two circles shown above are concentric with center O, which exp  [#permalink]

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11 Sep 2018, 02:58
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Difficulty:

35% (medium)

Question Stats:

72% (01:53) correct 28% (01:32) wrong based on 25 sessions

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If the two circles shown above are concentric with center O, which expression represents the area of the region ABDC in terms of the radius of the large circle R and the radius of small circle r and the measure of angle AOB x ?

A. $$\frac{\pi x}{360}(R - r)^2$$

B. $$\frac{\pi 180}{x}(R^2 - r^2)$$

C. $$\frac{\pi 360}{x}(R - r)^2$$

D. $$\frac{\pi 360}{x}(R^2 - r^2)$$

E. $$\frac{\pi x}{360}(R^2 - r^2)$$

Attachment:

image018.jpg [ 2.41 KiB | Viewed 621 times ]

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If the two circles shown above are concentric with center O, which exp  [#permalink]

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11 Sep 2018, 05:19
Bunuel wrote:

If the two circles shown above are concentric with center O, which expression represents the area of the region ABDC in terms of the radius of the large circle R and the radius of small circle r and the measure of angle AOB x ?

A. $$\frac{\pi x}{360}(R - r)^2$$

B. $$\frac{\pi 180}{x}(R^2 - r^2)$$

C. $$\frac{\pi 360}{x}(R - r)^2$$

D. $$\frac{\pi 360}{x}(R^2 - r^2)$$

E. $$\frac{\pi x}{360}(R^2 - r^2)$$

Attachment:
image018.jpg

Area of region ABDC = Bigger Sector - Smaller sector = $$\frac{\pi x}{360}(R^2 - r^2)$$

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Re: If the two circles shown above are concentric with center O, which exp  [#permalink]

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11 Sep 2018, 06:07
Should be E as no other one is sufficient
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Re: If the two circles shown above are concentric with center O, which exp  [#permalink]

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04 Mar 2019, 01:55
Area of sector = angle /360 * pi * r^2
so for large circle ; angle/360 * R^2 and small circle angle/360 * r^2
difference will give us the area of ABDC

IMO E $$\frac{\pi x}{360}(R^2 - r^2)$$

Bunuel wrote:

If the two circles shown above are concentric with center O, which expression represents the area of the region ABDC in terms of the radius of the large circle R and the radius of small circle r and the measure of angle AOB x ?

A. $$\frac{\pi x}{360}(R - r)^2$$

B. $$\frac{\pi 180}{x}(R^2 - r^2)$$

C. $$\frac{\pi 360}{x}(R - r)^2$$

D. $$\frac{\pi 360}{x}(R^2 - r^2)$$

E. $$\frac{\pi x}{360}(R^2 - r^2)$$

Attachment:
image018.jpg

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Re: If the two circles shown above are concentric with center O, which exp   [#permalink] 04 Mar 2019, 01:55
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