Friday, April 29, 2011

Geometry Problem 596: Quadrilateral, Right Triangle, Isosceles, Midpoint

Geometry Problem
Click the figure below to see the complete problem 596.

 Geometry Problem 596: Quadrilateral, Right Triangle, Isosceles, Midpoint.

2 comments:

  1. By applying Apollonius' theorem to triangle ACD and BCF to get two equations.
    Eliminating the length of CD, CF and BF will get 2x = 20.

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  2. http://img849.imageshack.us/img849/1084/problem596.png

    Draw lines per attached sketch
    We have ED=EB and CB=CD => CE is perpendicular bisector of BD
    ∆ EFC ≅ to ∆ EGC …..( Case SAS)
    Since E and G are midpoints of AD and CD => EG=1/2.AC=10
    So x=EF=EG=10

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