MathDB

P12

Part of 2018 Latvia Baltic Way TST

Problems(1)

Parallelogram with arbitrary segments, another parallelity needed

Source: 2018 Latvia BW TST P12

3/26/2022
Let ABCDABCD be a parallelogram. Let XX and YY be arbitrary points on sides BCBC and CDCD, respectively. Segments BYBY and DXDX intersect at PP. Prove that the line going through the midpoints of segments BDBD and XYXY is either parallel to or coincides with line APAP.
geometryparallelogram