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In the figure above, which of the following are true?
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30 Nov 2021, 06:44
30 Nov 2021, 06:44
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In the figure above, which of the following are true?
I. \(OP = OQ\)
II. \(\sqrt{PQ} < \sqrt{OP}\)
III. \(PQ > OQ\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
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Joined: 10 Apr 2015
Posts: 6218
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Re: In the figure above, which of the following are true?
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30 Nov 2021, 07:17
30 Nov 2021, 07:17
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Carcass wrote:
In the figure above, which of the following are true?
I. \(OP = OQ\)
II. \(\sqrt{PQ} < \sqrt{OP}\)
III. \(PQ > OQ\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Since the radii of a circle all have equal length, we know that OP = OQ, which means triangle OPQ is an isosceles triangle.
So, angle OQP must also equal 59 degrees, which means angle QOP = 62 degrees (since all three angles in a triangle must add to 180 degrees)
Now let's examine the statements....
I. \(OP = OQ\)
Since the radii of a circle all have equal length, we know that OP = OQ
So, statement I is TRUE
This means we can eliminate answer choices B and C since they state that statement I is not true.
IMPORTANT: When I scan statements II and III, I see that statement III is a little easier to deal with. So I'll analyze that statement next.
III. \(PQ > OQ\)
There's a nice triangle property that says: The side opposite the greatest angle is the longest side, and the side opposite the smallest angle is the shortest side (see video for more details)
Since 62 degrees is the greatest angle, we know that the side opposite (side PQ) is is the longest side.
So, statement III is TRUE
This means we can eliminate answer choices A and D since they state that statement II is not true.
By the process of elimination, the correct answer is E.
Re: In the figure above, which of the following are true?
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08 Jan 2023, 19:13
08 Jan 2023, 19:13
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
