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# In the figure given, line C is a diameter of the circle and parallel

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
In the figure given, line C is a diameter of the circle and parallel  [#permalink]

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22 Jul 2018, 22:43
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(N/A)

Question Stats:

79% (06:08) correct 21% (01:30) wrong based on 14 sessions

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In the figure given, line C is a diameter of the circle and parallel to line B. The distance between lines B and C is 2.5. The blue shaded portion, which is the sector formed by the endpoints of the chord on line B, is 1/3 of the area of the circle. What is the area of the green-shaded portion of the circle?

A. 6.5π
B. 7.5π
C. 8.5π
D. 9.5π
E. 10.5π

Attachment:

542.gif [ 7.56 KiB | Viewed 420 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7113
Re: In the figure given, line C is a diameter of the circle and parallel  [#permalink]

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23 Jul 2018, 02:14
Bunuel wrote:

In the figure given, line C is a diameter of the circle and parallel to line B. The distance between lines B and C is 2.5. The blue shaded portion, which is the sector formed by the endpoints of the chord on line B, is 1/3 of the area of the circle. What is the area of the green-shaded portion of the circle?

A. 6.5π
B. 7.5π
C. 8.5π
D. 9.5π
E. 10.5π

Attachment:
The attachment 542.gif is no longer available

1/3 area at centre means 360/3=120° at O
So blue portion makes a 120° angle at centre.
Draw a perpendicular OX so OX bisects the 120 angle therefore OXY becomes 30:60:90 triangle with sides OX:XY:OY in ratio 1:√3:2..
Now OX is 2.5, so OY is 2*OX=2*2.5=5 and OY is nothing but the radius
Area =π*5^2=25π

Now take the green portion..
The green portion makes a 108° angle at centre as lines are PARALLEL..
So if 360° has an area of 25π, 108° will have an area of 25π*108/360=25π*3/10=7.5π

B
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PicsArt_07-23-03.38.00.jpg [ 19.94 KiB | Viewed 324 times ]

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: In the figure given, line C is a diameter of the circle and parallel &nbs [#permalink] 23 Jul 2018, 02:14
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