Difference between revisions of "Routh's Theorem"
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==Proof== | ==Proof== | ||
− | + | Scale [[triangle]]<math>ABC</math>'s area down so that it becomes 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> |
+ | |||
+ | Full proof: https://en.wikipedia.org/wiki/Routh%27s_theorem | ||
== See also == | == See also == |
Latest revision as of 23:02, 23 March 2021
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
Scale triangle's area down so that it becomes 1. We can then use Menelaus's Theorem on triangle and line . This means
Full proof: https://en.wikipedia.org/wiki/Routh%27s_theorem
See also
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