Routh's Theorem
Revision as of 17:10, 18 August 2014 by Awesomedude102 (talk | contribs)
In triangle ,
,
and
are points on sides
,
, and
, respectively. Let
,
, and
. Let
be the intersection of
and
,
be the intersection of
and
, and
be the intersection of
and
. Then, Routh's Theorem states that
Proof
Assume triangle's area to be 1. We can then use Menelaus's Theorem on triangle
and line
.
This means $\frac{DG}{GA} = \frac{BR}{FA}\times\frac{DC}{CB} = \frac{rs}{s+1}
See also
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