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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Regards,

PKN

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