Friday, November 30, 2012

Problem 829: Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations

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

Click the figure below to see the complete problem 829.

Online Geometry Problem 829: Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

3 comments:

  1. Denote BF, BG by p & q resply. Use Stewart's Theorem to obtain: 125+x^2=6(p^2+5), 50+4x^2=6(q^2+8)and p/(p+5/p) =q/(q+8/q).
    Solve simultaneously to get x=5√(2.5) --- same as Atharva

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  2. Since DE//AC so Arc(AD)=Arc(EC) => angle (ABF)=angle(CBG)
    So in triangle ABC ,line BF and BG are isogonal to each other.
    Per Steiner’s theorem for isogonal lines BF and BG
    (AF/FC).(AG/GC)=AB^2/BC^2
    So 1/5 . 4/2 =25/x^2
    So x=5.sqrt(5/2)

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