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Question
If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is ______.
Options
130°
100°
50°
30°
Solution
If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is 100°.
Explanation:
OP ⊥ PR ...[Y Tangent and radius are ⊥ to each other at the point of contact]
∠OPQ = 90° – 50° = 40°
OP = OQ ...[Radii]
∴ ∠OPQ = ∠OQP = 40°
In ΔOPQ,
`\implies` ∠POQ + ∠OPQ + ∠OQP = 180°
`\implies` ∠POQ + 40° + 40° = 180°
∠POQ = 180° – 80° = 100°.
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