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Question

The diagonals of a parallelogram ABCD intersect at O. A line through O intersect AB at X and DC at Y. Identify the correct option
509064_224fd84437b64da4870e0c6353c78d16.png

A
OX=OY
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B
OX>OY
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C
OX<OY
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D
OXOY=0
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Solution

The correct option is C OX=OY
In given figure ABCD is a parallelogram.
ABDC
Also AC is a transversal of ABDC.
1=2 [Alternate interior angles]
Now in AXO and CYO, we have
1=2 [Alternate interior angles]
3=4 [Vertically opposite angles]
CO=OA [Diagonals bisect each other]
AXOCYO [ASA Criteria]
OX=OY [CPCT]

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