1997 OIM Problems/Problem 5
Problem
In an acute triangle , let and be two heights, and let be the orthocenter. The symmetrical line of with respect to the (interior) bisector of the angle at and the symmetrical line of with respect to the (interior) bisector of the angle at intersect at a point . The lines and intersect a second time the circumference circumscribes triangle at points and , respectively.
Let be the intersection of with ; , the intersection of with ; and the intersection of with .
Prove that is a parallelogram.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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