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RS Aggarwal Solutions Class 10 Mathematics Solutions for Circles Exercise 8B in Chapter 8 - Circles

Question 6 Circles Exercise 8B

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

Answer:

Since tangents are drawn from an external point are equally inclined to the line joining center to that point. Draw an image based on given instructions:

R S Aggarwal Solutions - Mathematics - Class 10 chapter  Circles Question 6 Solution image

Here, PT is the tangent of the circle OT ⊥ PT And, ∠TPS = 60° (given) ∠TPO = 60°/2 = 30° Now, from right ∆TPO: sin 30° = OT/OP 1/2 = a/OP or OP = 2a

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