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Question
In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is ______.
Options
45°
90°
60°
180°
Solution
In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is 90°.
Explanation:
Given, ∠OPQ = x, ∠POQ = y
∠OQP = 90° ...(∵ Radius is perpendicular to the tangent at the point of contact.)
In ΔOPQ,
∠OPQ + ∠POQ + ∠OQP = 180° ...(angle sum property)
`\implies` x + y + 90° = 180°
`\implies` x + y = 180° – 90° = 90°
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