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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.

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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 70o
Join 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 triangle
Now in ΔOPQ, by Angle sum property of a triangle
OPQ+OQP+POQ=180o
OPQ=OQP=35
Since PT is tangent OPT=90
QPT=9035=55=PQT
Now Δ PTQ,
PTQ+TPQ+TQP=180o
PTQ=180110=70

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