The angle formed between two tangents to a circle of radius 6 cm at an external point P is 60 degree, then the distance of the external point P from the centre is
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Answer:
Step-by-step explanation:
Ap=BP ....(length of tangents from external point to circle are equal)
∠A=∠B=90
o
.... (Tangent is ⊥ to radius)
OP=OP .... (common side)
∴△AOP≅△BOP ....(RHS test of congruence)
∠APO=∠BPO=30
o
→c.a.c.t
∠AOP=∠BOP=60
o
→c.a.c.t
△AOP is 30
o
−60
o
−90
o
triangle.
∴△AOP,
cos60=
OP
OA
OP=
2
1
a
=2a
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