Let $I$ be the incenter of a triangle $ABC$. A point $X$ satisfies the conditions $XA+XB=IA+IB$, $XA+XC=IA+IC$. The points $Y,Z$ are defined similarly. Show that the lines $AX,BY,CZ$ are concurrent or parallel to each other.
My friend discovered this problem when he was drawing random ellipses for fun. But we have no idea how to solve such a problem because we literally know nothing about ellipses (except its definition). So I can't post where I'm stuck here. We're just curious to see the solution, whether or not it's elementary.
We do not know what kind of tags we should add because we do not know what methods are to be used. Please edit the tagging.
No comments:
Post a Comment