MathDB

30

Part of 1988 IMO Longlists

Problems(1)

Mid-points of the three sides X,Y and Z

Source: IMO LongList 1988, Hong Kong 6, Problem 30 of ILL

10/22/2005
In the triangle ABCABC let D,ED,E and FF be the mid-points of the three sides, X,YX,Y and ZZ the feet of the three altitudes, HH the orthocenter, and P,QP,Q and RR the mid-points of the line segment joining HH to the three vertices. Show that the nine points D,E,F,P,Q,R,X,Y,ZD,E,F,P,Q,R,X,Y,Z lie on a circle.
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