## Show it parallel

For discussing Olympiad level Geometry Problems
tanmoy
Posts: 289
Joined: Fri Oct 18, 2013 11:56 pm

### Show it parallel

Take any point $P_{1}$ on the side $BC$ of a triangle $ABC$ and draw the following chain of lines:
$P_{1}P_{2}\parallel AC$,$P_{2}P_{3}\parallel BC$,$P_{3}P_{4}\parallel AB$,$P_{4}P_{5}\parallel CA$,$P_{5}P_{6}\parallel BC$.Here,$P_{2},P_{5}$ lie on $AB$;$P_{3},P_{6}$ lie on $CA$ and $P_{4}$ on $BC$.Show that,$P_{6}P_{1}$ $\parallel$ $AB$
"Questions we can't answer are far better than answers we can't question"

SANZEED
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