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.

Question

Philoid · Accepted Answer

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