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Question

If the angle between two tangents drawn from an external point P to a circle of radius a and a center O, is 60o , then find the length of OP.

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Solution

Ap=BP ....(length of tangents from external point to circle are equal)
A=B=90o .... (Tangent is to radius)
OP=OP .... (common side)
AOPBOP ....(RHS test of congruence)
APO=BPO=30oc.a.c.t
AOP=BOP=60oc.a.c.t
AOP is 30o60o90o triangle.
AOP,
cos60=OAOP
OP=a12=2a

667952_627717_ans_305f8fd8e8d243d89f236174d510221a.png

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