Wednesday, February 12, 2014

Geometry Problem 979: Triangle, Cevian, Angle Bisector, Concurrency, 90 Degrees, Perpendicular

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

Click the figure below to see the complete problem 979.

Online Geometry Problem 979: Triangle, Cevian, Angle Bisector, Concurrency, 90 Degrees, Perpendicular

1 comment:

  1. Applying Ceva’s theorem in triangle ABC
    DA/DC x FC/FB x EB/EA= 1…….(1)
    Replace DA/DC= DA/DB x DB/DC (2)
    Since DE is angle bisector of ∠(ADB ) => DA/DB= EA/EB
    Replace this in (2) and (1) and simplifying we have DB/DC x FC/FB= 1
    Or DB/DC= FB/FC => DF is angle bisector of ∠(BDC)
    ∠(EDF)=1/2 ∠(ADC) = 90

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