Answer :

The figure according to given information is as shown below



Consider ΔAQS and ΔBQC


QS = QC … given


SQA = CQB … vertically opposite angles


AQ = BQ … CQ is median on AB


Therefore, ΔAQS ΔBQC … SAS test for congruency


ASQ = BCQ … corresponding angles of congruent triangles


Thus AS || BC because ASQ and BCQ are pair of alternate interior angles with transversal as CS


AS || BC … (i)


Consider ΔAR and ΔCPB


BP = PR … given


APR = BPC … vertically opposite angles


AP = CP … BP is median on AC


Therefore, ΔAPR ΔCPB … SAS test for congruency


ARP = CBP … corresponding angles of congruent triangles


Thus AR || BC because ARP and CBP are pair of alternate interior angles with transversal as BR


AR || BC … (ii)


From (i) and (ii) we can say that


AS || AR


But point A lies on both the lines AS and AR which means AS and AR are on the same straight line


Thus, point A, S and R are collinear points


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