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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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Question Stats:

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

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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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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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] 07 Mar 2017, 15:37
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