What is the value of an angle subtended by a chord at the circle, if the angle subtended by this chord at the circumference is 66^o ?

132^o

Let O, C and AB be the centre, a point on the circumference and the chord respectively.

Hence, \(\angle\)ACB = \({66}^\circ\)

Here, \(\angle\)AOB is the angle subtended by the same chord, AB on the centre of the circle.

According to the concept,

\(\angle\)AOB = 2 x \(\angle\)ACB

⇒ \(\angle\)AOB = 2 x \({66}^\circ\)

⇒ \(\angle\)AOB = \({132}^\circ\)

Therefore, the angle subtended by the same chord on the centre of the circle is \({132}^\circ\).