Mathematics

Problem

Which of the following sets of conditions is sufficient to conclude that four distinct points

P, Q, R, S

are concyclic? a)

\angle PQS = \angle PRS

and both angles are on opposite sides of

PS

\angle PSQ = \angle PRQ

and both angles are on the same side of

PQ

PQ = QR

and

QR = RS

\angle PQS + \angle QRS = 180^{\circ}