Sunday, January 10, 2010

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

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

Routh's Theorem 1: Triangle, Cevians, Ratio, Areas.
See also:
Routh's Theorem 1
Level: High School, SAT Prep, College geometry

2 comments:

  1. draw from C, altitude h1 on AA', from B, alt h2 on AA'
    =>
    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)
    ---------------------------------------
    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)

    ReplyDelete
  2. To c.t.e.o:
    Your answer is correct. Thanks for your comments.

    ReplyDelete