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ASU 501 All Soviet Union MO 1989 collinear midpoints wanted

Source:

August 13, 2019
midpointscollinearrotationequal segments

Problem Statement

ABCDABCD has AB=CDAB = CD, but ABAB not parallel to CDCD, and ADAD parallel to BCBC. The triangle is ABCABC is rotated about CC to A′B′CA'B'C. Show that the midpoints of BC,B′CBC, B'C and A′DA'D are collinear.
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