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A Line Parallel to a Side of a Triangle

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Let ABC be a triangle. Let AD, BE, and CF be the altitudes and M be the midpoint of BC. Let the circumcircle of AEF meet AM at X, let AM meet CF at Y, and let AD meet BX at Z. Then YZ is parallel to BC.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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