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

Consider △POQ

AB || PQ ….[ Given ]

So, By basic proportionality theorem,

$\dfrac{OA}{AP} = \dfrac{OB}{BQ} \qquad \text{[….Eq 1]}$

Then consider △OPR

AC || PR ….[ Given ]

So, By basic proportionality theorem,

$\dfrac{OA}{AP} = \dfrac{OC}{CR} \qquad \text{[….Eq 2]}$

Comparing Eq 1 and Eq 2 we get,

$\Rightarrow \dfrac{OB}{BQ} = \dfrac{OC}{CR}$

Hence, by basic proportionality theorem BC || QR.