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If the angle between two tangents …

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If the angle between two tangents drawn from an external point P to a radius a and centre O, is 60° then find the length of OP. [CBSE 2017] Ans: a√3

    • Posted by Laxmi Narayan 4 years, 10 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 4 years, 10 months ago

    Ap=BP     ....(length of tangents from external point to circle are equal)

    ∠A=∠B=90o      .... (Tangent is ⊥ to radius) 

    OP=OP        .... (common side)

    ∴△AOP≅△BOP    ....(RHS test of congruence)

    ∠APO=∠BPO=30o→c.a.c.t

    ∠AOP=∠BOP=60o→c.a.c.t

    △AOP is 30o−60o−90o triangle.

    ∴△AOP, 

    cos60=OPOA​

    OP= ​a/ 1/2​=2a 

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