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Solution


Q.

In Fig. PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is:
1 45°  
2 90°  
3 60°  
4 180°  

Ans.

(2)

Since PQ is tangent at Q to the circle and OQ is radius,
∴ OQ ? PQ ⇒ ∠OQP = 90°

In ΔPOQ, we have

∠OQP + ∠OPQ + ∠POQ = 180°  [Angle Sum Property of triangle]

⇒ 90° + x + y = 180°
⇒ x + y = 180° – 90° = 90°