In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Given here,
In \(\triangle OPQ\), AB || PQ

By using Basic Proportionality Theorem,
\(\frac{OA}{AP} = \frac{OB}{BQ}\)…………….(i)

Also given,
In \(\triangle OPR\), AC || PR

By using Basic Proportionality Theorem
\(\frac{OA}{AP} = \frac{OC}{CR}\)……………(ii)

From equation (i) and (ii), we get,
\(\frac{OB}{BQ} = \frac{OC}{CR}\)

Therefore, by converse of Basic Proportionality Theorem,

In \(\triangle OQR\), BC || QR.