Wednesday, January 13, 2016

Geometry Problem 1177: Triangle, Two Angle Bisectors, Metric Relations

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

Click the figure below to view more details of problem 1177.

Online Math: Geometry Problem 1177: Triangle, Two Angle Bisectors, Metric Relations.

Posted by Antonio Gutierrez at 5:15 PM
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3 comments:

  1. Sumith PeirisJanuary 13, 2016 at 9:34 PM

    We can write 4 simple equations

    y+e = c.......(1)
    x+d = a........(2)
    c/b = x/d.......(3)
    a/b = y/e.......(4)

    Now we can eliminate a,b,c between these 4 equations.

    From (3') & (4) dc/x = ae/y and so from (1) and (2)
    d(y+e)/x = e(x+d)/y

    Simplifying x^2e + xde + y^2d + yde

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. APOSTOLIS MANOLOUDISJanuary 14, 2016 at 3:09 AM

    Manoloudis Apostolis 4 Lyceum of Korydallos-Greece
    Even AB=c BC=a AC=b.Then x.e.(x+d)=y.d.(y+e) x.e,a=y.d.c
    By theorem bisectors c/b=x/d and x=a.c/(b+c) d=a.b/(b+c) and a/b=y/e
    y=a.c/(a+b) e=b.c/(a+b).
    x.e.a=a.c/(b+c).b.c/(a+b).a=y.d.c .


    ReplyDelete
  3. c.t.e.oJanuary 14, 2016 at 9:25 AM

    apply two times bisector´s theorem
    First for AD, and second for CE

    ReplyDelete

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