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+1 vote
2.0k views
in Circles by (30.5k points)
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In Fig. if PR is tangent to the circle at P and Q is the centre of the circle, then ∠POQ =

A. 110° 

B. 100° 

C. 120° 

D. 90°

1 Answer

+2 votes
by (30.3k points)
selected by
 
Best answer

Answer is C. 120°

Given: 

∠RPQ = 60° 

Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency. 

Property 2: Sum of all angles of a triangle = 180°. 

By property 1, ∆OPR is right-angled at ∠OPR (i.e., ∠OPR = 90°). 

OP = OQ [∵ radius of circle] 

∴ ∠OPQ = ∠OQP = 30° 

Now by property 2, 

∠OPQ + ∠OQP + ∠POQ = 180° 

⇒ 30° + 30° + ∠POQ = 180° 

⇒ 60° + ∠POQ = 180° 

⇒ ∠POQ = 180° - 60° 

⇒ ∠POQ = 120° 

Hence, ∠POQ = 120°

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