Let ABCD be a parallelogram. Let X and Y be arbitrary points on sides BC and CD, respectively. Segments BY and DX intersect at P. Prove that the line going through the midpoints of segments BD and XY is either parallel to or coincides with line AP.
Source: 2018 Latvia BW TST P12
Tags: geometry, parallelogram
Let ABCD be a parallelogram. Let X and Y be arbitrary points on sides BC and CD, respectively. Segments BY and DX intersect at P. Prove that the line going through the midpoints of segments BD and XY is either parallel to or coincides with line AP.