We know that,
Radius ⊥ Tangent = OR ⊥ PR
i.e., ∠ORP = 90°
Likewise,
Radius ⊥ Tangent = OQ ⊥PQ
∠OQP = 90°
In quadrilateral ORPQ,
Sum of all interior angles = 360º
∠ORP + ∠RPQ+ ∠PQO + ∠QOR = 360º
90º + ∠RPQ + 90º + ∠QOR = 360º
Hence, ∠O + ∠P = 180o
PROQ is a cyclic quadrilateral.