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# In the circle, line segments AD, BE, and CF all pass through

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In the circle, line segments AD, BE, and CF all pass through [#permalink]  04 Mar 2017, 03:19
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00:00

Question Stats:

75% (00:59) correct 24% (01:12) wrong based on 62 sessions

Attachment:

#GREpracticequestion In the circle, line segments AD, BE, and CF.jpg [ 11.7 KiB | Viewed 1475 times ]

In the circle, line segments AD, BE, and CF all pass through center 0.

 Quantity A Quantity B The area of shaded sector BOC The area of shaded sector AOF

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: In the circle, line segments AD, BE, and CF all pass through [#permalink]  07 Mar 2017, 15:37
Expert's post
Explanation

The sector with the greatest central angle will have the greatest area.

Angle BOC is a vertical angle with angle EOF, so BOC also equals 42°.

Angle AOB + angle AOF + angle EOF = 180° (because BE is a straight line).

$$\angle AOB + \angle AOF + \angle EOF =180$$

$$95 + \angle AOF + 42 = 180$$

$$95+ \angle AOF + 42 = 180$$

$$137 + \angle AOF = 180$$

$$\angle AOF = 43$$

Because angle AOF is greater than angle BOC, sector AOF is greater. Hence option B is correct.
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Re: In the circle, line segments AD, BE, and CF all pass through [#permalink]  18 Feb 2019, 08:44
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Carcass wrote:

Attachment:
#GREpracticequestion In the circle, line segments AD, BE, and CF.jpg

In the circle, line segments AD, BE, and CF all pass through center 0.

 Quantity A Quantity B The area of shaded sector BOC The area of shaded sector AOF

Since angles on a line must add to 180°...

...we can conclude that ∠AOF = 43°

Since opposite angles are EQUAL...

...we can conclude that ∠BOC = 42°

We now have...

Since sector AOF has a greater central angle (43°) than sector BOC (42°), we can conclude that the AREA of sector AOF is greater than the AREA of sector BOC

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: In the circle, line segments AD, BE, and CF all pass through   [#permalink] 18 Feb 2019, 08:44
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