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Question

# In Figure If TP and TQ are the two tangents to a circle with centre O so that ∠POQ =110o, the ∠ PTQ is equal to.

A
60o
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B
70o
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C
80o
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D
90o
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Solution

## The correct option is A 70oJoin PQ in given figure then we have two triangles ΔOPQ and Δ PTQ, In ΔOPQ ,OP=OQ radius of triangle, and in Δ PTQ, PT=TQ (Property of circle, two tangents drawn from a point to a circle are equal), so Both triangles are isosceles triangleNow in ΔOPQ, by Angle sum property of a triangle⟹∠OPQ+∠OQP+∠POQ=180o∠OPQ=∠OQP=35∘ Since PT is tangent ∴∠OPT=90∘∴∠QPT=90∘−35∘=55∘=∠PQTNow Δ PTQ,∠PTQ+∠TPQ+∠TQP=180o⟹∠PTQ=180∘−110∘=70∘

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