$$\begin{gathered} i) Draw PQ \\ \angle PQR=90° \left( the angle at the circumeference substended by a diameter equals 90°\right) \\ \angle SPQ=\angle PQR \left(alternate angles are equal, SP\parallel QR\right) \\ =90° \\ \therefore SQ is a diameter (a right angle at the circumeference substends a diameter\left) \\ ii\right) If QS\parallel SR\hspace{0.17em}then PQRS is a paralle\log ram (both pairs of opposite sides are parallel) \\ \therefore PR=QS (opposite sides of a paralle\log ram are equal) \\ \therefore Both circles have equal diameters and hence equal radii) \end{gathered}$$