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# Circles of radius 2 and 3 are externally tangent and are circumscribed

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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19 Mar 2019, 00:01
00:00

Difficulty:

5% (low)

Question Stats:

96% (01:04) correct 4% (00:50) wrong based on 23 sessions

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Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.

(A) $$3\pi$$

(B) $$4\pi$$

(C) $$6\pi$$

(D) $$9\pi$$

(E) $$12\pi$$

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2c5a7bbafa30af5c988825a58d564ad2037aaa7b.png [ 20.54 KiB | Viewed 427 times ]

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Joined: 04 Jan 2015
Posts: 3158
Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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19 Mar 2019, 00:18

Solution

Given:
• Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the given diagram.

To find:
• The area of the shaded region.

Approach and Working:
Diameter of the third (biggest) circle = diameter of first circle + diameter of second circle = 6 + 4 = 10
• Therefore, radius of the third circle = 5
• So, area of the shaded region = area of the third circle – (area of first circle + area of second circle) = π(5)2 – [π(2)2 + π(3)2] = 25π – 13π = 12π

Hence, the correct answer is option E.

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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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19 Mar 2019, 02:28
IMO E

Radious of big circle = 5

so area of two small circles = 13π

area of big circele = 25 π

so area of shaded region = 25 π - 13π = 12π

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Concentration: Sustainability, Marketing
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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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19 Mar 2019, 03:52
[quote="Bunuel"]
Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.

(A) $$3\pi$$

(B) $$4\pi$$

(C) $$6\pi$$

(D) $$9\pi$$

(E) $$12\pi$$

area = 25pi
small circle area = 9pi+4pi = 13 pi
shaded region = 25pi-13pi = 12pi
IMO E
Re: Circles of radius 2 and 3 are externally tangent and are circumscribed   [#permalink] 19 Mar 2019, 03:52
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