Parallelogram

Let PQ and RS be two diagonals of a circle with center as O, and tangents through their end points make a quadrilateral ABCD.

Now, we know that Tangent at any point is perpendicular to the radius at the point of contact

OR ⊥ CD and OS ⊥ AB

⇒ ∠ORD = ∠OSB [Both 90°]

⇒ AB || CD [If two lines are cut by a transversal and the alternate interior angles are equal, then the lines are parallel]

Also,

OP ⊥ AD and OQ ⊥ BC

⇒ ∠APQ = ∠CQP [Both 90°]

⇒ AD || BC [If two lines are cut by a transversal and the alternate interior angles are equal, then the lines are parallel]

⇒ In quadrilateral ABCD, opposite sides are parallel

⇒ ABCD is a parallelogram.