Question

Question 6
In the following figure, 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 $\Delta OPQ,AB||PQ$ (Given)
$\therefore \frac{OA}{AP}=\frac{OB}{BQ}...\left(i\right)$ [By using Basic Proportionality Theorem]
In $\Delta OPR,AC||PR$ (Given)
$\therefore \frac{OA}{AP}=\frac{OC}{CR}...\left(ii\right)$ [By using Basic Proportionality Theorem]
From equation (i) and (ii), we get
$\frac{OB}{BQ}=\frac{OC}{CR}$
Therefore, in $\Delta OQR,BC||QR$. [By converse of Basic Proportionality Theorem].