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Question:

In 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:

In ΔPOR, PR || AC (Given)
By basic proportionality theorem, PA/AO = RC/CO (1)
Similarly, In ΔPOQ, AB || PQ (Given)
By basic proportionality theorem, PA/AO = QB/BO (2)
From (1) and (2), RC/CO = QB/BO
By converse of basic proportionality theorem, BC || QR (hence proved)