# If PT is a tangent to a circle with center O and PQ is a chord of the circle such that ∠QPT = 70°, then find the measure of ∠POQ.

Given: PT is a tangent to a circle with center O and PQ is a chord of the circle such that QPT = 70°

To Find: POQ = ?

Now,

OPT = 90°

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

OPQ + QPT = 90°

OPQ + 70° = 90°

OPQ = 20°

Also,

OP = OQ [Radii of same circle]

OQP = OPQ = 20°

[Angles opposite to equal sides are equal]

In OPQ By Angle sum property of triangles,

OPQ + OQP + POQ = 180°

20° + 20° + POQ = 180°

POQ = 140°

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