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Parallel lines inside a square

Source: Sharygin 2014 Correspondence Round

January 8, 2015

geometry unsolvedgeometry

Problem Statement

Points

K, L, M

and

N

lying on the sides

AB, BC, CD

and

DA

of a square

ABCD

are vertices of another square. Lines

DK

and

N M

meet at point

E

, and lines

KC

and

LM

meet at point

F

. Prove that

EF\parallel AB

.

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