JEE Advance - Mathematics (1980 - No. 4)
$$ABC$$ is a triangle with $$AB=AC$$. $$D$$ is any point on the side $$BC$$. $$E$$ and $$F$$ are points on the side $$AB$$ and $$AC$$, respectively, such that $$DE$$ is parallel to $$AC$$, and $$DF$$ is parallel to $$AB$$. Prove that
$$$DF + FA + AE + ED = AB + AC$$$
The statement is always true.
The statement is true only if D is the midpoint of BC.
The statement is true only if triangle ABC is equilateral.
The statement is true only if angle BAC is a right angle.
The statement is false.
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