Question

If PA and PB are two tangents to a circle with center 0, from a point P outside the circle, such that <AOP = 60, then < APB =​

Answer 1

Answer:

< APB =60°

Step-by-step explanation:

In the figure PA and PB are tangents from same point P So

PA =PB

and ∠PAO=∠PBO=90° ( The nagle between tangent and radius is 90)

So in Δ PAO

∠ OPA=90-60=30°

Now in the Δ PAO and Δ POB

PA=PB

∠PAO=∠PBO=90°

and OA=OB=r

Thus Δ PAO ≅ Δ POB

So the ∠OPB= ∠OPA =30

Thus the < APB =∠OPB+ ∠OPA

=30+30=60°

< APB =60°

Answer 2

Answer:

< APB = 60°

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