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Points A, B, C, D, E, and F lie, in that order, on \(\overline {AF}\), dividing it into five segments, each of length 1. Point G is not on the line through A and F. Point H lies on \(\overline {GD}\), and point J lies on \(\overline {GF}\). The line segments \(\overline {HC}\)\(\overline {JE}\), and \(\overline {AG}\) are parallel. Find \(\displaystyle\frac{HC}{JE}\).

 Oct 4, 2021
 #1
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By similar triangles, HC/JE = 7/5.

 Oct 4, 2021
 #2
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∠GAF = ∠HCD = ∠JEF = 45º

 

HC = √2

 

JE = √72 / 10

 

HC / JE = 5/3

 Oct 5, 2021
edited by civonamzuk  Oct 5, 2021

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