If angle subtended by a chord on the major arc of a circle is 55 degree, then what will be the angle subtended by the same chord on the centre of the circle ?
Answer & explanation
Correct answer: option 4
⇒ Let O, C and AB be the centre, a point on the major arc, and the aforementioned chord respectively.
So, the major arc for the AB chord is ACB.
Hence, \(\angle\)ACB = \({55}^\circ\)
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 \({55}^\circ\)
⇒ \(\angle\)AOB = \({110}^\circ\)
Therefore, the angle subtended by the same chord on the centre of the circle is \({110}^\circ\).