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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
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The length of arc AXB is twice the length of arc BZC, and the length o
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31 Mar 2021, 21:17
31 Mar 2021, 21:17
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The length of arc AXB is twice the length of arc BZC, and the length of arc AYC is three times the length of arc AXB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
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Joined: 16 Apr 2020
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Posts: 1546
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The length of arc AXB is twice the length of arc BZC, and the length o
[#permalink]
31 Mar 2021, 22:40
31 Mar 2021, 22:40
GeminiHeat wrote:
Attachment:
Arcs.gif
The length of arc AXB is twice the length of arc BZC, and the length of arc AYC is three times the length of arc AXB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Let \(O\) be the centre of the circle
\(AXB + BZC + CYA = 2πr\)
\(2(BZC) + BZC + 3(2BZC) = 2πr\)
\(9BZC = 2πr\)
\(BZC = \frac{2}{9}πr\)
Let the angle subtended by \(BZC\) be \(x\)
\(BZC = \frac{x}{360}(2πr)\)
Therefore, \(\frac{x}{360}(2πr) = \frac{2}{9}πr\)
\(x = 40\)
i.e. \(∠BOC = 40\), \(∠BOA = 80\), and \(∠AOC = 240\)
Using Central Angle property:
\(∠BCA = \frac{1}{2}∠BOA\)
\(∠BCA = \frac{1}{2}(80) = 40\)
Hence, option B
gmatclubot
The length of arc AXB is twice the length of arc BZC, and the length o [#permalink]
31 Mar 2021, 22:40
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