Geometry Problem

Click the figure below to see the complete problem 596.

## Friday, April 29, 2011

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## Friday, April 29, 2011

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

## Link List

Online Geometry theorems, problems, solutions, and related topics.

Labels:
congruence,
isosceles,
midpoint,
quadrilateral,
right triangle

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By applying Apollonius' theorem to triangle ACD and BCF to get two equations.

ReplyDeleteEliminating the length of CD, CF and BF will get 2x = 20.

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

ReplyDeleteDraw 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