# Concurrency Proof

Prove that the line joining the midpoints of opposite sides of a quadrilateral and the line joining the midpoints of the diagonals are concurrent.

I haven't really done concurrency proofs before, but I guess the first part is because the midpoints of sides of any quadrilateral form a parallelogram and diagonals of a parallelogram are concurrent. I need some help with the second part.

Addendum- In any triangle $ABC$, prove that the bisectors of the interior angle $A$ and exterior angles at $B$ and $C$ are concurrent.

• Since the Addendum has nothing to do with the original question, it "should" be posted separately; however, since you've already provided an answer, it doesn't matter. I'll note that the Addendum follows immediately from the trigonometric form of Ceva's Theorem. – Blue Oct 9 '16 at 13:18