Thursday, May 17, 2012

Problem 753: Triangle, Altitudes, Orthocenter, Sum of ratios

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the problem 753 details.

Online Geometry Problem 753: Triangle, Altitudes, Orthocenter, Sum of ratios.

Posted by Antonio Gutierrez at 4:22 PM
Labels: , , ,

1 comment:

  1. PravinMay 17, 2012 at 5:17 PM

    DH/AD = (BHD)/(BAD) = (CHD)/(CAD)
    = Sum of numerators/sum of denominators
    =[(BHD)+(CHD)]/[(BAD)+(CAD)]
    =(BHC)/(ABC)
    Similarly
    EH/BE = (AHC)/(ABC)& FH/CF = (ABH)/(ABC)
    Hence
    DH/AD + EH/BE + FH/CF
    =[(BHC)+(AHC)+(ABH)]/(ABC)
    =(ABC)/(ABC)
    = 1
    Remark: Result holds for any interior point P,
    not necessarily H.

    ReplyDelete

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