Wednesday, July 2, 2008

Elearn Geometry Problem 133



See complete Problem 133
Triangle, Angle Bisectors, Collinear Points. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. AE is an interior bisector of angle A
    BE/EC = AB/AC
    CD is an interior bisector of angle C
    AD/DB = AC/BC
    AE is an exterior bisector of angle B
    FA/FC = AB/BC
    therefore
    BD/DA * AF/FC * CE/EB = BC/AC * AB/BC * AC/BC = 1
    therefore
    D, E, F are collinear points
    Magdy Essafty

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  2. - P is on AC such that BP bisects <B.
    - It is known that P is the harmonic conjugate of F w/r AC.
    In conclusion, F-E-D must be colinear.

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