Let ABCDEF be a convex hexagon satisfying AB || DE, BC || EF, CD || FA,...

 

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Let ABCDEF be a convex hexagon satisfying AB || DE, BC || EF, CD || FA, and AB DEBC EF = CD. FA. Let X, Y, and Z be the midpoints of AD, BE, and CF. Prove that the circumcenter of AACE, the circumcenter of ABDF, and the orthocenter of AXYZ are collinear. Let ABCDEF be a convex hexagon satisfying AB || DE, BC || EF, CD || FA, and AB DEBC EF = CD. FA. Let X, Y, and Z be the midpoints of AD, BE, and CF. Prove that the circumcenter of AACE, the circumcenter of ABDF, and the orthocenter of AXYZ are collinear.