# In the given figure, O is the center of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70°, then ∠TPQ is equal toA. 35°B. 45°C. 55°D. 70°

In OPQ

POQ = 70° [Given]

OP = OQ [radii of same circle]

OQP = OPQ [Angles opposite to equal sides are equal]

By angle sum Property of triangle,

POQ + OQP + OPQ = 180°

70° + OPQ + OPQ = 180°

2 OPQ = 110°

OPQ = 55°

Now,

OPT = 90°

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

OPQ + TPQ = 90°

55° + TPQ = 90°

TPQ = 35°

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