(Q23) In the given figure A, B and C are points on OP, OQ and OR respectively such that AB ∥ PQ and AC ∥ PR. Show that BC ∥ QR.

Solution :

Given :In ∆PQR, AB ∥ PQ; AC ∥ PR

R.T.P : BC ∥ QR

Proof : In ∆POQ, AB ∥ PQ

(∵ Basic Proportional theorem)

and in ∆OPR,

From (1) and (2), we can write

Then consider above condition in ∆OQR then from (3) it is clear.

∴ BC ∥ QR [∵ from converse of Basic Proportionality Theorem]

Hence Proved.