Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the complete problem 979.
Wednesday, February 12, 2014
Geometry Problem 979: Triangle, Cevian, Angle Bisector, Concurrency, 90 Degrees, Perpendicular
Subscribe to:
Post Comments (Atom)
Applying Ceva’s theorem in triangle ABC
ReplyDeleteDA/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