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Sub 505 (Easy)|   Geometry|         
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Bunuel
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If O is the center of the circle above and the length of arc RSP is tw 03 Aug 2018, 03:52
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

85% (01:06) correct 15% (01:34) wrong based on 231 sessions

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If O is the center of the circle above and the length of arc RSP is twice the length of arc PQR, then x equals

(A) 60
(B) 100
(C) 120
(D) 150
(E) 240

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Screen Shot 2015-03-10 at 1.53.19 PM.png
Screen Shot 2015-03-10 at 1.53.19 PM.png [ 16.04 KiB | Viewed 5782 times ]
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C
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If O is the center of the circle above and the length of arc RSP is tw 03 Aug 2018, 04:02
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Angle POR=x
Outside angle (maybe incorrect interpretation) POR=2x

x+2x=360
x=120

IMO
Ans: C
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If O is the center of the circle above and the length of arc RSP is tw 03 Aug 2018, 07:56
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Bunuel

If O is the center of the circle above and the length of arc RSP is twice the length of arc PQR, then x equals

(A) 60
(B) 100
(C) 120
(D) 150
(E) 240
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\(\widehat{PQR}\)+\(\widehat{RSP}\)=\(Circumference=2\pi*r\)
Or, \(\widehat{PQR}\)+2*\(\widehat{PQR}\)=\(2\pi*r\)
Or, 3*\(\widehat{PQR}\)=\(2\pi*r\)
Or, \(3*2\pi*r(x/360)\)=\(2\pi*r\)
Or, \(x=\frac{360}{3}\)
Or, x=120

Ans. (C)
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If O is the center of the circle above and the length of arc RSP is tw 15 Dec 2018, 12:10
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2 + 1 = 3, then 360 degrees has to be divided into three, two of these parts are RSP and one part is PQR. Which makes x = 360/3 = 120.
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If O is the center of the circle above and the length of arc RSP is tw 27 Aug 2020, 06:26
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Given

    • O is the center of the circle above and the length of arc RSP is twice the length of arc PQR.


To Find

    • The value of x.

Approach and Working Out

    • The ratio of smaller arc (PQR) to the larger arc (PSR) = 1: 2.

    • The ratio of angle will be same.
      o Total angle is 360
      o x = \(\frac{1}{3 }\)× 360
      o x = 120

Correct Answer: Option C
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If O is the center of the circle above and the length of arc RSP is tw 16 Apr 2022, 09:57
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