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Founder  Joined: 18 Apr 2015
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O is the center [#permalink]
Expert's post 00:00

Question Stats: 91% (01:02) correct 8% (02:04) wrong based on 56 sessions
Attachment: #GREpracticequestion O is the center of the circle.png [ 134.62 KiB | Viewed 499 times ]

O is the center of the circle and ∠AOC is a right angle

 Quantity A Quantity B OD BD

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

_________________ Director  Joined: 07 Jan 2018
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Re: O is the center [#permalink]
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Explanation

In this figure, if $$<BDC = 90$$ degrees than $$<BDO$$ should be $$90$$ degrees as well.
This is because angle in a straight line add to $$180$$ degree

Similarly, If $$<AOB = 44$$degrees than $$<BOD = 46$$ degrees because Given $$AOC$$ is a right triangle so $$<AOB$$ and $$<BOD$$ should add to $$90$$degrees

Now the remaining angle$$<DBO = 44$$ degrees
Sum of angles in a triangle add to $$180$$ degrees.

From here we can deduce that $$BD>OD$$ because side opposite larger angle is larger than side opposite smaller angle in a triangle
option B
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes GRE Instructor Joined: 10 Apr 2015
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Re: O is the center [#permalink]
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Expert's post
Carcass wrote:
Attachment:
circle.png

O is the center of the circle and ∠AOC is a right angle

 Quantity A Quantity B OD BD

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.

Given: ∠AOC = 90°
So, if ∠AOB = 44°, then ∠BOD = 46°

If ∠BOD = 46°, then ∠OBD = 44° (since all 3 angles in ∆OBD must add to 180°

Notice that side OD is opposite the 44° angle (aka ∠OBD),
and side BD is opposite the 46° angle (aka ∠BOD)

Since 46° > 44°, we can conclude that side BD > side OD

Answer: B

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Director Joined: 09 Nov 2018
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Re: O is the center [#permalink]
Opposite of larger angle is larger side

B Re: O is the center   [#permalink] 19 Jan 2019, 16:24
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