Bunuel wrote:

What is the measure of angle AOB in the circle with center O?

(1) Major arc AB is greater than 180°.

(2) Minor arc AB is 1/11 of the circumference.

Question stem: \(\angle{AOB}\)=?

St1:-

Major arc AB is greater than 180°.Greatest measure of an arc of a circle is the measure of circumference, i.e, \(2\pi*r\)

Given, Major Arc \(AB>\pi\)

So,\(\pi\)<Arc AB <\(2\pi*r\)

No unique value of arc AB as measure of radius is not known and length of arc AB is a variant.

And measure of \(\angle{AOB}\) is dependent on the measure of arc AB.

Therefore, insufficient.

St2:-

Minor arc AB is 1/11 of the circumferenceOr, Minor Arc AB=\(\frac{2\pi*r}{11}\)

\(\angle{AOB}\) formed by minor arc AB=\(\frac{Arc_{AB}}{Radius}\)=\(\frac{\frac{2\pi*r}{11}}{r}=\frac{2\pi}{11}\)

Sufficient.

Ans. (B)

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine