IMO 1988 LL HKG35

In the triangle ABC, let D, E, and F be the midpoints of the

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IMO 1988 LL HKG35

Origin: HKG

Problem

In the triangle ABC, let D, E, and F be the midpoints of the three sides, X, Y , and Z the feet of the three altitudes, H the orthocenter, and P, Q, and R the midpoints of the line segments joining H to the three vertices. Show that the nine points D, E, F, P, Q, R, X, Y, Z lie on a circle.