Q. 114.1( 15 Votes )

ABCD is a paralle

Answer :

We have the diagram as


Given: DP = PC &


CQ = (1/4)AC …(i)


To Prove: CR = RB


Proof: Join B to D


As diagonals of a parallelogram bisect each other at S.


…(ii)


Dividing equation (i) by (ii), we get




CQ = CS/2


Q is the midpoint of CS.


According to midpoint theorem in ∆CSD, we have


PQ DS


Similarly, in ∆CSB, we have


QR SB


Also, given that CQ = QS


We can conclude that, by the converse of midpoint theorem, CR = RB.


That is, R is the midpoint of CB.


Hence, proved.


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