Solution :
Given : O is any point within triangle PQR, AB || PQ and AC || PR
To Prove : BC || QR
Construction : Join BC
Proof : In triangle OPQ,
Given, AB || PQ
By basic proportionality theorem,
\(OA\over AP\) = \(OB\over BQ\) ………..(1)
In triangle OPR,
Given, AC || PR
By basic proportionality theorem,
\(OA\over AP\) = \(OC\over CR\) ………..(2)
From (1) and (2), we obtain that
\(OB\over BQ\) = \(OC\over CR\)
Hence, by converse of basic proportionality theorem, we have
BC || QR