Question

the correct answer is option (a)

show the method also

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Answer 1

GOOD MORNING.... ☺️

Answer:AE

Solution:

We know that,

Centroid of a triangle is the point of intersection of the medians of a triangle and also centroid of a triangle divides each median in the ratio 2:1.

Then,
We get,

AE/OE=2/1 and
CF/OF=2/1

AE=2OE......1. and
CF=2OF..............2

We know diagonals of a parallelogram bisect each other.

Therefore,
AO=OC
AE+OE=CF+OF

By eq1 and eq2 we get,

2OE+OE=2OF+OF
3OE=3OF
OE=OF........................3

Similarly we can prove,
AE=CF.........................4

By eq1,eq2,eq3,eq4 we get,
AE=2OE=2OF=CF..................5

Now,
We have
OE+OF=OE+OE. (by eq3)
EF=2OE
EF=AE. (by eq 5)