Problem: Let $ABC$ be a triangle.
Take noncollinear points $D$, $E$, $F$ on the perpendicular bisectors
of $BC$, $CA$, $AB$ respectively.
Show that the lines through $A$, $B$, $C$
perpendicular to $EF$, $FD$, $DE$ respectively are concurrent.

Solution: The three lines are the radical axii of the three circles
centered at $D$, $E$, $F$, so they concur.