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Comparison of Lengths of Arcs

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yasir9909
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Comparison of Lengths of Arcs [#permalink] New post   02 Oct 2016, 09:10
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\(x>y\)

Quantity A
Quantity B
Length of Arc PRQ
Length of Arc QPR



    A : Quantity A is greater
    B : Quantity B is greater
    C : Both quantities are equal
    D : Answer Cannot be determined
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B
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yasir9909
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Re: Comparison of Lengths of Arcs [#permalink] New post   02 Oct 2016, 09:52
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Angles x and y are inscribed angles and in any given circle,an arc with a larger inscribed angle is longer than an arc with a smaller inscribed angle.
So as x>y => Arc PQ > Arc QR
But arcs listed in Quantities A and B are different,each of them is a full circle with one section removed

Quantity A : Circumference minus the Arc with inscribed angle x (a longer arc PQ)
Quantity A : Circumference minus the Arc with inscribed angle y (a shorter arc QR)

In other words Arc QPR is missing less of the circumference than the Arc PRQ,thus Arc QPR is longer than Arc PRQ

This question has been taken from tests of Greatest Prep.Here is the link to the website of Greatest Prep : http://www.greatestprep.com
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Comparison of Lengths of Arcs [#permalink] New post   15 Aug 2019, 17:53
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yasir9909 wrote:
Image

\(x>y\)

Quantity A
Quantity B
Length of Arc PRQ
Length of Arc QPR



Here's what we're comparing.
Image
Quantity A is the length of the BLUE arc, and Quantity B is the length of the RED arc.

Since both arcs contain the same PURPLE arc shown below....
Image
....we can IGNORE that portion of the arc and make things easier by comparing these two arcs:
Image


At this point, we can see that ...
Image
... angle y is an inscribed angle "holding" (aka "containing") the BLUE arc,
and angle x is an inscribed angle "holding" (aka "containing") the RED arc

Since we're told that angle x is greater than angle y, we know that the RED arc is longer than the BLUE arc.

In other words, Quantity B is greater than Quantity A

Answer: B

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Re: Comparison of Lengths of Arcs [#permalink] New post   09 Sep 2019, 15:27
This says basically the same as what's gone before.
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sides and sectors of triangles.jpg
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Re: Comparison of Lengths of Arcs [#permalink] New post   13 Dec 2023, 15:10
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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Re: Comparison of Lengths of Arcs [#permalink]
13 Dec 2023, 15:10
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