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Alley Ladders

Problem

Two ladders are placed on opposite diagonals in an alley such that one ladder reaches $a$ units up one wall, the other ladder reaches $b$ units up the opposite wall and they intersect $h$ units above the ground.


Prove the following result.

 1 
$ a$
 + 
 1 
$ b$
 = 
 1 
$ h$
Problem ID: 127 (Oct 2003)     Difficulty: 3 Star

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