A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110° and 130°, respectively. Then the value of ∠BAC is:
Answer & explanation
Correct answer: option 3
From the following figure,
\(\angle\)AOB = \({110}^\circ\) and \(\angle\)AOC = \({130}^\circ\)
As we know,
\(\angle\)AOB + \(\angle\)AOC + \(\angle\)BOC = \({360}^\circ\)
\(\angle\)BOC = \({360}^\circ\) - \({110}^\circ\) - \({130}^\circ\) = \({120}^\circ\)
\(\angle\)BAC = \(\angle\)BOC/2
Therefore, \(\angle\)BAC = \(\frac{120}{2}\) = \({60}^\circ\).