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Comparison of Lengths of Arcs
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02 Oct 2016, 09:10
02 Oct 2016, 09:10
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Question Stats:
50% (01:11) correct
49% (01:11) wrong based on 85 sessions
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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
Re: Comparison of Lengths of Arcs
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02 Oct 2016, 09:52
02 Oct 2016, 09:52
2
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
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
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15 Aug 2019, 17:53
15 Aug 2019, 17:53
3
yasir9909 wrote:
\(x>y\)
Quantity A |
Quantity B |
Length of Arc PRQ |
Length of Arc QPR |
Here's what we're comparing.
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....
....we can IGNORE that portion of the arc and make things easier by comparing these two arcs:
At this point, we can see that ...
... 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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