Angle subtended by a chord AB on the centre of the circle is 140 degree. What will be the angle subtended by the chord AB on the major are of the circle?
Answer & explanation
Correct answer: option 4
The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle circumference
Take any point Q on the circumference and join AQ and QC.
Therefore, \(\angle\)AOC = 2 x \(\angle\)AQC
= \(\angle\)AQC = \(\frac{1}{2}\) x \(\angle\)AOC = \(\frac{1}{2}\) x \({140}^\circ\) = \({70}^\circ\)
Now, \(\angle\)CBP = \(\angle\)AQC [Exterior angle of cyclic quadrilateral]
= \(\angle\)CBP = \({70}^\circ\)