Question : The angle subtended by an arc at the circumference of the circle is 55°. Find the angle subtended by it at the centre.
Option 1: 35°
Option 2: 110°
Option 3: 125°
Option 4: 27.5°
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Correct Answer: 110°
Solution :
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Let O, R, and PQ be the centre, a point on the major arc, and the aforementioned chord respectively.
So, the major arc for the PQ chord is PRQ.
So, $\angle$PRQ = 55°
Here, $\angle$POQ is the angle subtended by the same chord, PQ on the centre of the circle.
According to the concept,
$\angle$POQ = 2 × $\angle$PRQ
⇒ $\angle$POQ = 2 × 55°
⇒ $\angle$POQ = 110°
Hence, the correct answer is 110°.
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