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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, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 8 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

1Thank You

ANSWER

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