Angle subtended by a chord on the major arc of a circle is 65 degree. What is the angle subtended by the same chord on the centre of this circle ?
Answer & explanation
Correct answer: option 1
Let O, R and PQ be center, a point on the major arc and the aforementioned chord respectively.
So, the major arc for the PQ chord is PRQ.
Hence, \(\angle\)PRQ = \({65}^\circ\)
\(\angle\)POQ is the angle subtended by the same chord, PQ on the center of the circle.
According to the concept,
\(\angle\)POQ = 2 x \(\angle\)PRQ
= \(\angle\)POQ = 2 x \({65}^\circ\)
= \(\angle\)POQ = \({130}^\circ\)
Therefore, the angle subtended by the same chord on the center of the circle is \({130}^\circ\).