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# 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.