Monday, November 28, 2016

Geometry Problem 1289 Triangle, Cevian, Concurrency, Measurement, Metric Relations

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1289 Elements: Triangle, Cevian, Concurrency, Measurement, Metric Relations.

Posted by Antonio Gutierrez at 7:56 AM
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3 comments:

  1. APOSTOLIS MANOLOUDISNovember 28, 2016 at 10:50 AM

    Problem 1289
    From Ceva’s theorem BF/FA.AE/EC.CD/DB=1, from Menelaus
    Theorem BF/FA.AG/GC.CD/DB=1 then BF/FA.AE/EC.CD/DB=BF/FA.AG/GC.CD/DB or AE/EC=AG/GC or
    5/3=(8+x)/x or x=12.
    APOSTOLIS MANOLOUDIS 4 HIGH SCHOOL KORYDALLOS PIRAEUS GREECE

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  2. Peter TranNovember 28, 2016 at 6:20 PM

    Observe that AFDCBG is a complete quadrilateral with diagonals AD and FC met at O
    So E and G are the harmonic conjugate of A and C or (ACEG)=-1
    and EC/EA=GC/GA=3/5= x/(x+8) => x= 12

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  3. UnknownDecember 18, 2016 at 5:50 PM

    https://en.wikipedia.org/wiki/Projective_harmonic_conjugate A,E,C,G form a system of Harmonic Conjugate points therefore 3/5=(x/x+8) -->x=12

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