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TP is a line that tangent to a circle centered at O. If PQ∥TO and ∠OTP=28∘, find the measure of ∠POQ in degrees.

 

 Jun 17, 2021
 #1
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Let the tangent to the circle be TPR then, 

∠OTP = ∠QPR = 28°         ...[PQ∥TO and corres. angles] 

 

OP ⊥ TR       ...[TR is a tangent and OP is the radius] 

⇒ ∠OPR = 90°

 ∠OPQ = ∠OPR -  ∠QPR = 90 - 28 = 62

 ∠OPQ = 62° 

 

∵ OP = OQ           ...[radii of circle] 

⇒ ∠OPQ = ∠OQP = 62°

In △OPQ

 ∠OPQ +  ∠OQP + ∠POQ = 180 

                               ∠POQ = 180 - 124 

                               ∠POQ = 56°

 Jun 17, 2021
 #2
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TP is a line that tangent to a circle centered at O. If PQ∥TO and ∠OTP=28∘, find the measure of ∠POQ in degrees.

 Jun 17, 2021

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