If a straight line meets the sides BC, CA, and AB
of a triangle ABC
in the points D, E, and F respectively
then (AE/EC)* (CD/DB)* (BF/FA) = 1.
Prove the above theorem.
BTW the converse is also true.
Some consider me good,
and some consider me bad.
Some gather in my house,
because I am a part of a fad.
Sometimes I am dark.
and sometimes I am light.
I could be the savior at sunrise,
and sometimes the savior of night.
What am I?