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# The circle shown has center T. The measure of angle TVU is 60°. If the

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The circle shown has center T. The measure of angle TVU is 60°. If the  [#permalink]

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16 Oct 2018, 01:06
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The circle shown has center T. The measure of angle TVU is 60°. If the circle has a radius of 3, what is the length of segment RS?

A. 2

B. $$2 \sqrt{2}$$

C. 3

D. $$3 \sqrt{3}$$

E. $$6 \sqrt{2}$$

Attachment:

circle.jpg [ 9.34 KiB | Viewed 605 times ]

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The circle shown has center T. The measure of angle TVU is 60°. If the  [#permalink]

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Updated on: 16 Oct 2018, 09:56
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Bunuel wrote:

The circle shown has center T. The measure of angle TVU is 60°. If the circle has a radius of 3, what is the length of segment RS?

A. 2

B. $$2 \sqrt{2}$$

C. 3

D. $$3 \sqrt{3}$$

E. $$6 \sqrt{2}$$

TVU is an equilateral triangle(TU=TV=radius, angle TUV=angle TUV=60, angle UTV=180-60-60=60)

Note:- The Angles subtended by same arc at the circumference are equal. So, under arc SV, Angle SRV=angle SUV or TUV=60.

Now, join SV. RSV is a right angled triangle(60-90-30)
Hence the sides are in the ratio, SV:RV:RS= √3x:2x:x
RS=2x=6 or x=3

Therefore, RS=x=3

Ans. (C)

Edit:- I don't know why I took radius=2 instead of 3.. drinking
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Originally posted by PKN on 16 Oct 2018, 08:12.
Last edited by PKN on 16 Oct 2018, 09:56, edited 1 time in total.
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The circle shown has center T. The measure of angle TVU is 60°. If the  [#permalink]

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16 Oct 2018, 09:43
TU = TV = 60 each. Therefore it's an equilateral triangle.
RTS = 60 (opposite angle)
RT = ST = 60 each. Therefore it's an equilateral triangle.

RT = radius = 3 = RS

Ans C

PKN , 2x = 6 ; not 4
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Re: The circle shown has center T. The measure of angle TVU is 60°. If the  [#permalink]

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16 Oct 2018, 09:57
pandeyashwin wrote:
TU = TV = 60 each. Therefore it's an equilateral triangle.
RTS = 60 (opposite angle)
RT = ST = 60 each. Therefore it's an equilateral triangle.

RT = radius = 3 = RS

Ans C

PKN , 2x = 6 ; not 4

Thank you a ton.
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PKN

Rise above the storm, you will find the sunshine
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Re: The circle shown has center T. The measure of angle TVU is 60°. If the  [#permalink]

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17 Oct 2018, 19:02
Bunuel wrote:

The circle shown has center T. The measure of angle TVU is 60°. If the circle has a radius of 3, what is the length of segment RS?

A. 2

B. $$2 \sqrt{2}$$

C. 3

D. $$3 \sqrt{3}$$

E. $$6 \sqrt{2}$$

Attachment:
circle.jpg

For triangle TUV, we know that both sides TV and TU are 3 (because they are both radii of the circle). Thus, both angles TVU and TUV are 60 degrees, meaning that angle UTV is also 60 degrees, and thus triangle TUV is equilateral.

We know that angle UTV equals angle RTS. Using similar logic, we also can determine that triangle RTS is equilateral, and thus, segment RS = 3.

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Re: The circle shown has center T. The measure of angle TVU is 60°. If the   [#permalink] 17 Oct 2018, 19:02
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