If the angle between two radii of a circle is $130^\circ$, then the angle between the tangents at the ends of the radii is:
(a) $50^\circ$
(b) $90^\circ$
(c) $40^\circ$
(d) $60^\circ$
Step-by-Step Solution
Key Concept: The angle between two tangents drawn from an external point and the angle subtended by the line segments joining points of contact at the centre are supplementary: $\theta + 130^\circ = 180^\circ \Rightarrow \theta = 50^\circ$.
Angle between tangents $+ 130^\circ = 180^\circ \Rightarrow \text{Angle} = 180^\circ - 130^\circ = 50^\circ$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating angle $= 50^\circ$: 1.0 Mark
Correct Answer: $50^\circ$