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
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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.