ABCD is a parallelogram such that its diagonals intersect each other at O. A line segment EOF is drawn such that it meets AB at E and DC at F then

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OE = 2OF

OE = OF

OF = 2OE

None of the above

answer is B.

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Detailed Solution

Given ABCD is a parallelogram such that its diagonals intersect each other at O. A line segment EOF is drawn such that it meets AB at E and DC at F.
Consider parallelogram ABCD,
Question Image

Consider

Δ O D F

and

Δ O B E

from the figure given.

∠ F D O = ∠ O B E

... (alternate interior angles)

∠ D O F = ∠ B O E

... (vertically opposite angles)
OD = OB ... (diagonals bisect each other)
By AAS rule for congruency,

Δ O D F ≅ Δ O B E

.
OF = OE ... by CPCT
So, if a line segment EOF is drawn such that it meets AB at E and DC at F, then OF = OE.
Therefore, option 2 is the correct choice.

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