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AB and CD are both diameters of a circle with centre O. So A, B, C, D

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AB and CD are both diameters of a circle with centre O. So A, B, C, D  [#permalink]

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New post 04 Jul 2018, 23:20
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

83% (01:29) correct 17% (01:29) wrong based on 18 sessions

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AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.
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Re: AB and CD are both diameters of a circle with centre O. So A, B, C, D  [#permalink]

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New post 04 Jul 2018, 23:53
amanvermagmat wrote:
AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.


Questions like these, which talk about a figure without giving it, are much easier to answer if we draw them out first.
This is an Alternative approach.

(1) Drawing a circle with two diameters and writing in AOD = 100, we can fill the angle opposite to it to be 100. Since the 4 angles sum to 360, the remaining two sum to 360 - 200 = 160.
So sectors AOC and BOD are proportional to 160 degrees of the circle meaning they have 160/360 of the area.
Sufficient.

(2) repeating the same process as above gives us exactly the same values.
Sufficient.

(D) is our answer.
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Re: AB and CD are both diameters of a circle with centre O. So A, B, C, D  [#permalink]

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New post 05 Jul 2018, 01:04
Quote:
amanvermagmat wrote:
AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.



Please refer the affixed diagram for the explanation.

Both statements are alone sufficient.

Ans. (D)
Attachments

Sector.JPG
Sector.JPG [ 34.55 KiB | Viewed 231 times ]


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Re: AB and CD are both diameters of a circle with centre O. So A, B, C, D &nbs [#permalink] 05 Jul 2018, 01:04
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