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655-705 (Hard)|   Geometry|      
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Bunuel
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What is the measure of angle AOB in the circle above with center O and 14 Sep 2018, 02:05
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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65% (hard)

Question Stats:

48% (01:50) correct 52% (01:50) wrong based on 54 sessions

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What is the measure of angle AOB in the circle above with center O and inscribed triangle ABC?

(1) The length of AB equals that of BC
(2) The measure of angle ACB is half the measure of angle AOB


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What is the measure of angle AOB in the circle above with center O and 14 Sep 2018, 02:32
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Bunuel

What is the measure of angle AOB in the circle above with center O and inscribed triangle ABC?

(1) The length of AB equals that of BC
(2) The measure of angle ACB is half the measure of angle AOB


Show Spoiler
Attachment:
image010.gif
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S1 - AB=BC
\(\angle\) ABC=90 [AC is diameter and ABC is angle in a semicircle]
\(\angle\) ACB=\(\angle\) CAB = 45
Triangles AOB and COB are similar, \(\angle\) AOB=\(\angle\)COB=90
Sufficient.

S2 = \(\angle\)ACB=\(\frac{1}{2}\)\(\angle\)AOB
Insufficient.
Answer A.
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What is the measure of angle AOB in the circle above with center O and 28 Jan 2020, 04:34
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Bunuel

What is the measure of angle AOB in the circle above with center O and inscribed triangle ABC?

(1) The length of AB equals that of BC
(2) The measure of angle ACB is half the measure of angle AOB


Show Spoiler
Attachment:
image010.gif

S1 - AB=BC
\(\angle\) ABC=90 [AC is diameter and ABC is angle in a semicircle]
\(\angle\) ACB=\(\angle\) CAB = 45
Triangles AOB and COB are similar, \(\angle\) AOB=\(\angle\)COB=90
Sufficient.

S2 = \(\angle\)ACB=\(\frac{1}{2}\)\(\angle\)AOB
Insufficient.
Answer A.
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Can you explain S2? chetan2u
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What is the measure of angle AOB in the circle above with center O and Updated on: 28 Jan 2020, 05:18
Originally posted by GMATinsight on 28 Jan 2020, 05:03.
Last edited by GMATinsight on 28 Jan 2020, 05:18, edited 1 time in total.
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exc4libur
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Bunuel

What is the measure of angle AOB in the circle above with center O and inscribed triangle ABC?

(1) The length of AB equals that of BC
(2) The measure of angle ACB is half the measure of angle AOB


Show Spoiler
Attachment:
The attachment image010.gif is no longer available

S1 - AB=BC
\(\angle\) ABC=90 [AC is diameter and ABC is angle in a semicircle]
\(\angle\) ACB=\(\angle\) CAB = 45
Triangles AOB and COB are similar, \(\angle\) AOB=\(\angle\)COB=90
Sufficient.

S2 = \(\angle\)ACB=\(\frac{1}{2}\)\(\angle\)AOB
Insufficient.
Answer A.

Can you explain S2? chetan2u
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exc4libur

Well, I am not Chetan yet I am taking my chance to explain it to you.

Property of circle suggests that any angle drawn at center of the circle is always twice the angle drawn at the circumference if the angles are drawn by the same arc/chord/segment of circle Check property 2 in the attachment. This property only leads us to the conclusion that any angle drawn at the circumference in semicircle is 90 degrees

Statement 2 suggests what we know already in form of this property hence it is redundant to answer the question

I hope that helps!!!
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What is the measure of angle AOB in the circle above with center O and 28 Jan 2020, 05:10
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GMATinsight

Property of circle suggests that any angle drawn at center of the circle is always twice the angle drawn at the circumference if the angles are drawn by the same arc/chord/segment of circle Check property 2 in the attachment. This property only leads us to the conclusion that any angle drawn at the circumference in semicircle is 90 degrees

Statement 2 suggests what we know already in form of this property hence it is redundant to answer the question

I hope that helps!!!
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GMATinsight thank you very much! I totally missed this :(
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What is the measure of angle AOB in the circle above with center O and 28 Jan 2020, 06:48
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Isn't the question stem by itself sufficient to answer this?

OA = OB (radii), so subtend an angle of 45 (OAB and OBA). This leaves AOB as 90 in all cases.

Or are we to consider that AC doesn't necessarily pass through the centre O?

Posted from my mobile device
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What is the measure of angle AOB in the circle above with center O and 28 Jan 2020, 07:27
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HYQ
Isn't the question stem by itself sufficient to answer this?

OA = OB (radii), so subtend an angle of 45 (OAB and OBA). This leaves AOB as 90 in all cases.

Or are we to consider that AC doesn't necessarily pass through the centre O?

Posted from my mobile device
Show more


HYQ

Nowhere does the question stem say that angle AOB = 90 degrees so you can NOT reach to the conclusion that angle OAB and OBA are 45º each


AC does pass through the center by B is not necessarily the midpoint of Arc ABC


I hope that helps!!! :)
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