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Let the intersection of lines

and

be denoted

. Let the line through point P and parallel to the line

be denoted by [P,

Let ABC and A'B'C' be two triangles. Let

, and

. Let

, and

. Then XX', YY', and ZZ' are concurrent.

Contributed by: Jay Warendorff

After work by: Darij Grinberg

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An Application of the Gergonne-Euler Theorem