The side MN of a parallelogram MNOP is produced to Q such that MN = NQ. PQ intersects ON at R. The point R divides ON in the ratio:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1 : 1.
MN = NQ
Here, MN = PO then, MN = PO = NQ
PO || MN then, PO || NQ

In ΔPOR and ΔNQR,
PO = NQ
∠OPR = ∠RQN (Alternate interior angles)
∠PRO = ∠QRN (Vertically opposite angles)
So, ΔOPR ≅ ΔNQR (ASA Rule)
Then, OR = RN
OR : RN = 1 : 1
Therefore, the point R divides ON in the ratio of 1 : 1.