Proposed Problem

Click the figure below to see the complete Routh's Theorem 1 about Triangle, Cevians, Ratio, Areas.

See also:

Routh's Theorem 1

Level: High School, SAT Prep, College geometry

## Sunday, January 10, 2010

### Routh's Theorem 1: Triangle, Cevians, Ratio, Areas

Labels:
area,
Ceva's theorem,
cevian,
Menelaus' theorem,
ratio,
Routh's theorem,
triangle

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draw from C, altitude h1 on AA', from B, alt h2 on AA'

ReplyDelete=>

h1/h2 = k => SAA'C/ABA' = k =>

SAA'C/S = k/(1+k)

In the same way

SABB'/S = m/(1+m) (1)

draw from B'//AA' => alt from B' on AA' is h3=(m/(1+m))h1

SADB = AD∙h2 = AD∙(h1/k)

SADB'= AD∙h3 =AD∙((m/(1+m))h1

=>

SADB'/SADB = k∙m/(1+m)

SABB'/SADB =(km + m + 1)/(1 + m)

(m/(1+m))/SADB = (km + m + 1)/(1 + m)

SADB = m /(km + m + 1)

for m = n = k = 1/2 SADB = 2/7 (P416, the niciest for me)

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there is a difference between my answer and P answer

is OK my conclusion

verify please

why is not displayed in main web page (propposed P)

To c.t.e.o:

ReplyDeleteYour answer is correct. Thanks for your comments.