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22 Nov 2019, 03:25
Kudos
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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:
55%
(hard)
Question Stats:
61% (02:25) correct
39%
(02:42)
wrong
based on 109
sessions
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Not Attempted Yet
The center of the circle is 0, and RS = ST = 4. What is the length of arc RWT?
A. \(\frac{4 \pi}{3}\)
B. \(\frac{8 \pi}{3}\)
C. \(\frac{16 \pi}{3}\)
D. \(4 \pi\)
E. \(8 \pi\)
Attachment:
1.jpg [ 19.91 KiB | Viewed 12017 times ]
06 Dec 2019, 00:40
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According to me,
Join OS ,OR and OT
we know OS =OR=OT=r
Consider triangle ORS
OR=OS =r
=> Angle ORS= Angle OSR ( angles opp to equal sides)
Similarly in triangle OST
OS=OT=r
=> Angle OST= OTS
But OS=OR=OT
=> angle ors= angle osr = angle ost = angle ots
Given=> Angle RST = 120
=> as angle OST = angle OSR
Angle OST = 60
=> in triangle OST
ANGLE OST = ANGLE OTS ( as proved above)
Angle ots =60
=> angle sot =60 ( by angle sum prop of triangle)
Therefore triangle OST is an equilateral triangle as all angles are equal
=> os=ot=st =4
Similarly Triangle ORS Is equilateral triangle
=>rs=or=os =4
Now , calculating
For arc RWT
(Angle /360)* 2*pi*r=( 240/360) *2* pi* 4
= > 16Pi/3
Therefore option C
Correct me if I am wrong, otherwise Kudos.
Posted from my mobile device
Join OS ,OR and OT
we know OS =OR=OT=r
Consider triangle ORS
OR=OS =r
=> Angle ORS= Angle OSR ( angles opp to equal sides)
Similarly in triangle OST
OS=OT=r
=> Angle OST= OTS
But OS=OR=OT
=> angle ors= angle osr = angle ost = angle ots
Given=> Angle RST = 120
=> as angle OST = angle OSR
Angle OST = 60
=> in triangle OST
ANGLE OST = ANGLE OTS ( as proved above)
Angle ots =60
=> angle sot =60 ( by angle sum prop of triangle)
Therefore triangle OST is an equilateral triangle as all angles are equal
=> os=ot=st =4
Similarly Triangle ORS Is equilateral triangle
=>rs=or=os =4
Now , calculating
For arc RWT
(Angle /360)* 2*pi*r=( 240/360) *2* pi* 4
= > 16Pi/3
Therefore option C
Correct me if I am wrong, otherwise Kudos.
Posted from my mobile device
General Discussion
Archit3110
22 Nov 2019, 03:56
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radius = 4 = RS= ST
angle = 120 *2 ; 240
2 * 4* pi * 240/360 = \(\frac{16 \pi}{3}\)
IMO C
angle = 120 *2 ; 240
2 * 4* pi * 240/360 = \(\frac{16 \pi}{3}\)
IMO C
Bunuel
