# In the given figure, PQ is a chord of a circle with center 0 and PT is a tangent. If ∠QPT = 60°, find ∠P

Given : , PQ is a chord of a circle with center 0 and PT is a tangent and QPT = 60°.

To Find : PRQ

OPT = 90°

OPQ + QPT = 90°

OPQ + 60° = 90°

OPQ = 30° … [1]

Also.

OP = OQ [radii of same circle]

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

From [1], OQP = OQP = 30°

In OPQ , By angle sum property

OQP + OPQ + POQ = 180°

30° + 30° + POQ = 180°

POQ = 120°

As we know, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

So, we have

2PRQ = reflex POQ

2PRQ = 360° - POQ

2PRQ = 360° - 120° = 240°

PRQ = 120°

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