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# O is the center

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O is the center [#permalink]  17 Mar 2018, 03:48
Expert's post
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Question Stats:

86% (00:57) correct 13% (01:10) wrong based on 171 sessions
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#GREpracticequestion O is the center of the circle.png [ 134.62 KiB | Viewed 4285 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

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Re: O is the center [#permalink]  17 Mar 2018, 23:07
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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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Re: O is the center [#permalink]  03 May 2018, 09:47
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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

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Re: O is the center [#permalink]  19 Jan 2019, 16:24
Opposite of larger angle is larger side

B
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Re: O is the center [#permalink]  12 Jul 2020, 05:22
Nice it is B.
We can determine which side is greater by its correspondent angle.
BD is bigger since its correspondent angle is 46
and OD is smaller since its correspondent angle is 44
Re: O is the center   [#permalink] 12 Jul 2020, 05:22
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