If angle between two radii of a circle is $130^\circ$, then the angle between the tangents at the ends of the radii is:
(a) $90^\circ$
(b) $50^\circ$
(c) $70^\circ$
(d) $40^\circ$
Step-by-Step Solution
Key Concept: The angle between the two tangents and the angle subtended by the radii at the center are supplementary ($180^\circ$).
$\text{Angle between tangents} + 130^\circ = 180^\circ$. [0.5 Mark]
$\text{Angle between tangents} = 180^\circ - 130^\circ = 50^\circ$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Stating supplementary relationship: 0.5 Mark
Calculating $180^\circ - 130^\circ = 50^\circ$: 0.5 Mark
Correct Answer: $50^\circ$