Question

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

Answer 1

In $△OPQ$, we have

$AB\parallel PQ$

Therefore, by using basic proportionality theorem , we have

$\frac{OA}{AP}=\frac{OB}{BQ}.................\left(i\right)$

IN $△OPR$, we have

$AC\parallel PR$

Therefore, by using basic proportionality theorem , we have

$\frac{OC}{CR}=\frac{OA}{AP}.................\left(ii\right)$

Comparing (i)&(ii), we get

$\frac{OB}{BQ}=\frac{OC}{CR}$

Therefore, by using converse of basic proportionality theorem, we get

$BC\parallel QR$