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# The center of the circle is 0, and RS = ST = 4. What is the length of

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

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22 Nov 2019, 03:25
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45% (medium)

Question Stats:

73% (02:28) correct 27% (02:37) wrong based on 49 sessions

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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 836 times ]

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Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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22 Nov 2019, 03:56
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
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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23 Nov 2019, 01:42
I have forgotten the formulas of circles. Can anyone explain the answer to me?

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

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23 Nov 2019, 03:08
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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Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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04 Dec 2019, 11:22
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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Joined: 18 Feb 2019
Posts: 14
Re: The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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06 Dec 2019, 00:16
2
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?

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Intern
Joined: 18 Feb 2019
Posts: 14
The center of the circle is 0, and RS = ST = 4. What is the length of  [#permalink]

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06 Dec 2019, 00:40
4
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.

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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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