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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] New post 04 Mar 2017, 03:19
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Question Stats:

85% (00:55) correct 15% (00:56) wrong based on 40 sessions



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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] New post 07 Mar 2017, 15:37
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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] 07 Mar 2017, 15:37
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In the circle, line segments AD, BE, and CF all pass through

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