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5

Part of 1997 Iran MO (3rd Round)

Problems(1)

D, E, I are collinear <=> P, Q, O are collinear

Source: Iran Third Round MO 1997, Exam 3, P5

6/30/2012
In an acute triangle ABCABC let ADAD and BEBE be altitudes, and APAP and BQBQ be bisectors. Let II and OO be centers of incircle and circumcircle, respectively. Prove that the points D,ED, E, and II are collinear if and only if the points P,QP, Q, and OO are collinear.
geometrycircumcirclegeometry proposed