Question

In below Fig, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = 1/4 AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.

Answer 1

Join B and D, suppose AC and BD out at O. 

Then OC = 1/2AC 

Now, 

CQ =1/4 AC