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If PA and PB are two tangents to a circle with centre O such that ∠APB = 80°. then, ∠AOP = ?

(a) 40°

(b) 50°

(c) 60°

(d) 70°

1 Answer

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Best answer

Given, PA and PB are two tangents to a circle with center O and ∠APB = 80°

\(\therefore \angle APO=\frac{1}{2}\angle APB=40^\circ\)

[Since they are equally inclined to the line segment joining the center to that point and ∠OAP = 90°]

[Since tangents drawn from an external point are perpendicular to the radius at the point of contact]

Now, in triangle AOP:

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