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A Line Parallel to a Side of a Triangle
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.



See Nice Parallelism.


"A Line Parallel to a Side of a Triangle" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ALineParallelToASideOfATriangle/
Contributed by: Jay Warendorff
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