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Solution


Q.

In Fig, from an external point P, two tangents PQ and PR are drawn to a circle of radius 4 cm with centre O. If ∠QPR = 90°, then length of PQ is:
1 3 cm  
2 4 cm  
3 2 cm  
4 22cm  

Ans.

(2)

Construction: Join OR as shown in

We have, ΔOQP ≅ ΔORP (by SSS congruency rule)∴ ∠OPQ = ∠OPR = 45°(by CPCT) (∵ ∠QPR = 90°)In ΔPOQ, ∠OQP = 90°, ∠OPQ = 45°∠POQ=180°-(90°+45°)=45°∴ ∠OPQ = ∠POQ = 45°∴ ∠OPQ = ∠POQ = 45° ⇒ OQ = PQ (Opposite sides of equal angles are equal)⇒PQ=4 cm