Sunday, June 8, 2008

Elearn Geometry Problem 115



See complete Problem 115
Area of Triangles, Excircles. Level: High School, SAT Prep, College

Post your solutions or ideas in the comments.
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2 comments:

  1. AnonymousJanuary 3, 2010 at 2:30 AM

    S=r_A(p-a)=r_B(p-b)=r_C(p-c)
    S1=S2=0.5r_C(p-c)
    S3=S4=0.5r_A(p-a)
    S5=S6=0.5r_B(p-b)
    .-.

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  2. W. Teddy .A .DApril 9, 2010 at 12:10 AM

    AM = BF = s-c
    S1=1/2.rc.AM =1/2.rc.(s-c)=1/2.([ABC]/(s-c)).(s-c)
    = 1/2.[ABC]
    S2=1/2.rc.BF =1/2.rc.(s-c)=1/2.([ABC]/(s-c)).(s-c)
    = 1/2.[ABC]
    Then S1=S2

    CH = BE = s-a
    S3=1/2.ra.CH =1/2.ra.(s-a)=1/2.([ABC]/(s-a)).(s-a)
    = 1/2.[ABC]
    S4=1/2.ra.BE =1/2.ra.(s-a)=1/2.([ABC]/(s-a)).(s-a)
    = c
    Then S1=S2=S3=S4

    with the way , it can be proved that :
    S5=S6=1/2.[ABC] so
    S1=S2=S3=S4=S5=S6=1/2.[ABC]

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