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# Find the area of common portion when two circles intersect as shown be

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Find the area of common portion when two circles intersect as shown be  [#permalink]

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Updated on: 26 Aug 2018, 02:38
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Difficulty:

65% (hard)

Question Stats:

48% (01:47) correct 52% (01:48) wrong based on 38 sessions

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Find the area of common portion when two circles intersect as shown below

(1) Distance between the centers of two circle is $$2\sqrt{2}$$.

(2) Arcs in common portion subtend 90 degree angle at the centers of respective circles.

Attachment:

Intersection1.jpg [ 13.47 KiB | Viewed 697 times ]

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Originally posted by Helium on 25 Aug 2018, 22:35.
Last edited by Bunuel on 26 Aug 2018, 02:38, edited 3 times in total.
Renamed the topic and edited the question.
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Re: Find the area of common portion when two circles intersect as shown be  [#permalink]

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25 Aug 2018, 23:41
1
Harshgmat wrote:
Find the area of common portion when two circles intersect as shown below

A) Distance between the centers of two circle is $$2\sqrt{2}$$.

B) Arcs in common portion subtend 90 degree angle at the centers of respective circles.

S1 - Circles may not be of same radius.
Insufficient.
S2 - Means circles have same radius, but no value given.
Insufficient.
Combining, since Distance between the centers of two circle is $$2\sqrt{2}$$ and the circles are of same radius.
We can find the radius, subsequently we can find the area of common portion.
Sufficient.

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Re: Find the area of common portion when two circles intersect as shown be  [#permalink]

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26 Aug 2018, 00:43
souvonik2k wrote:
Harshgmat wrote:
Find the area of common portion when two circles intersect as shown below

A) Distance between the centers of two circle is $$2\sqrt{2}$$.

B) Arcs in common portion subtend 90 degree angle at the centers of respective circles.

S1 - Circles may not be of same radius.
Insufficient.
S2 - Means circles have same radius, but no value given.
Insufficient.
Combining, since Distance between the centers of two circle is $$2\sqrt{2}$$ and the circles are of same radius.
We can find the radius, subsequently we can find the area of common portion.
Sufficient.

Hi souvonik2k,

After combining the above two statements also, we will get two values for r. Please correct me if I am wrong.

Scenario I: The two common arcs may pass through each other centres. Hence, $$r = 2\sqrt{2}.$$
Scenario II: The two arcs may not pass through each other centres, Here, $$r # 2\sqrt{2}.$$

Hence, E.
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Re: Find the area of common portion when two circles intersect as shown be  [#permalink]

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26 Aug 2018, 03:33
Can someone elaborate more on this question? I still dont know how to calculate the common area when combining stt1 & 2. My choice here is E.

Thank you so much
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Re: Find the area of common portion when two circles intersect as shown be  [#permalink]

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27 Aug 2018, 03:36
rahul16singh28 wrote:
souvonik2k wrote:
Harshgmat wrote:
Find the area of common portion when two circles intersect as shown below

A) Distance between the centers of two circle is $$2\sqrt{2}$$.

B) Arcs in common portion subtend 90 degree angle at the centers of respective circles.

S1 - Circles may not be of same radius.
Insufficient.
S2 - Means circles have same radius, but no value given.
Insufficient.
Combining, since Distance between the centers of two circle is $$2\sqrt{2}$$ and the circles are of same radius.
We can find the radius, subsequently we can find the area of common portion.
Sufficient.

Hi souvonik2k,

After combining the above two statements also, we will get two values for r. Please correct me if I am wrong.

Scenario I: The two common arcs may pass through each other centres. Hence, $$r = 2\sqrt{2}.$$
Scenario II: The two arcs may not pass through each other centres, Here, $$r # 2\sqrt{2}.$$

Hence, E.

Hi rahul16singh28
Refer to the attachment below. The line joining the centers is $$2\sqrt{2}$$ and each angle is 45 deg.
With that info, we can find the radius of the circle, since it is a rt. angled triangle with two angles 45 deg and one angle 90 deg.
Attachments

Untitled.png [ 4.58 KiB | Viewed 570 times ]

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Re: Find the area of common portion when two circles intersect as shown be   [#permalink] 27 Aug 2018, 03:36
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