Q15 of 95 Page 15

In Fig. 14.99, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ= AC. If PQ produced meets BC at R, Prove that R is a mid-point of BC.

Given,


Join B and D suppose AC and BD cut at D



Then, OC =


Now, CQ =


= CQ = =


In ∆DCO, P & Q are midpoints of DC & OC


∴ PQ


Also in ∆COB , Q is mid point of OC and QR││OB


∴ R is mid point of BC


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