Question

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

Answer 1

In $△$OPQ, we have

AB $\parallel$ PQ

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

$△$OQR, we have

BC $\parallel$ QR

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

From (i) and (ii), we get

$\frac{OA}{AP}$ = $\frac{OC}{CR}$ ...... (ii)
Thus, A and C are points on sides OP and OR respectively of $△$OPR, such that

$\frac{OA}{AP}$ = $\frac{OC}{CR}$ AC $\parallel$PR [Using the converse of BPT]