Difference between revisions of "Routh's Theorem"
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Assume [[triangle]]<math>ABC</math>'s area to be 1. We can then use Menelaus's Theorem on [[triangle]]<math>ABD</math> and line <math>FHC</math>. | Assume [[triangle]]<math>ABC</math>'s area to be 1. We can then use Menelaus's Theorem on [[triangle]]<math>ABD</math> and line <math>FHC</math>. | ||
<math>\frac{AF}{FB}\times\frac{BC}{CD}\times\frac{DG}{GA} = 1</math> | <math>\frac{AF}{FB}\times\frac{BC}{CD}\times\frac{DG}{GA} = 1</math> | ||
− | This means <math>\frac{DG}{GA} = \frac{ | + | This means <math>\frac{DG}{GA} = \frac{BF}{FA}\times\frac{DC}{CB} = \frac{rs}{s+1}</math> |
== See also == | == See also == |
Revision as of 17:34, 3 November 2014
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
See also
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