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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.


Solution

In ΔOPQ,AB||PQ (Given)
OAAP=OBBQ...(i) [By using Basic Proportionality Theorem]
In ΔOPR,AC||PR (Given)
OAAP=OCCR...(ii) [By using Basic Proportionality Theorem]
From equation (i) and (ii), we get
OBBQ=OCCR
Therefore, in ΔOQR,BC||QR. [By converse of Basic Proportionality Theorem].

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