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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The center of the circle is 0, and RS = ST = 4. What is the length of

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Math Expert V
Joined: 02 Sep 2009
Posts: 59721
The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (02:20) correct 29% (02:42) wrong based on 42 sessions

### HideShow timer Statistics 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 655 times ]

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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1
radius = 4 = RS= ST
angle = 120 *2 ; 240
2 * 4* pi * 240/360 = $$\frac{16 \pi}{3}$$
IMO C

Bunuel wrote: 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
Intern  B
Joined: 28 Nov 2017
Posts: 12
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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I have forgotten the formulas of circles. Can anyone explain the answer to me?

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Manager  B
Joined: 24 Jul 2019
Posts: 154
Location: Austria
GPA: 3.9
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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Archit3110 wrote:
radius = 4 = RS= ST
angle = 120 *2 ; 240
2 * 4* pi * 240/360 = $$\frac{16 \pi}{3}$$
IMO C

Bunuel wrote: 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

How do you know that R is the radius in this case?
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Director  V
Joined: 27 May 2012
Posts: 947
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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Bunuel wrote: 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

Can anybody explain this one , how is the radius = 4 ?
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Intern  B
Joined: 18 Feb 2019
Posts: 11
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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1
Archit3110 wrote:
radius = 4 = RS= ST
angle = 120 *2 ; 240
2 * 4* pi * 240/360 = $$\frac{16 \pi}{3}$$
IMO C

Bunuel wrote: 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

How have you considered radius to be 4?

Posted from my mobile device
Intern  B
Joined: 18 Feb 2019
Posts: 11
The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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3
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 The center of the circle is 0, and RS = ST = 4. What is the length of   [#permalink] 06 Dec 2019, 00:40
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