ImPerfectHacker has requested that I set a problem this week so here it is:

Problem of the Week 5

Given any four distinct points $\displaystyle A,\ B,\ C,\ O$, show that the three angles between the bisectors of $\displaystyle \angle AOB$, $\displaystyle \angle BOC$ and $\displaystyle \angle COA$ are all acute, right or obtuse.

RonL

(Clarification: the bisectors are of the non-reflex angles that correspond to the specified points)