Exams › SSC CGL (Prelims) › General

The angle between two tangents drawn from an external point to a circle is $75^\circ$. What is the angle subtended by the chord joining their points of contact at the center?

1. 75 $^\circ$
2. 105 $^\circ$
3. 90 $^\circ$
4. 150 $^\circ$

Correct answer: 105 $^\circ$

Solution

If two tangents from an external point make an angle of $75^\circ$, then the angle subtended by the chord at the center is $180^\circ - 75^\circ$. Therefore, the required angle is $105^\circ$.

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