1. The problem statement, all variables and given/known data A quadrilateral is given, and inside it connecting opposite sides are 2 lines which bisect the sides they connect. Prove that the bisectors bisect each other. 2. Relevant equations None. 3. The attempt at a solution Well I gave the sides lengths of 2q, 2r, 2s and 2p so that when it was bisected the lengths would be nice. I know that the bisectors are not necessarily parallel to any side, which if they were the proof would be simple. None of the angles are necessarily equal or even related in any way other than that they all add up to 2pi. I also realised that the bisectors are necessarily perpendicular to each other. It seems all I do is show what I can't assume! I also tried to draw out pairs of sides to a certain point to form a big triangle, because I thought I might be able to do something with similarity, but to no avail. Euclidean geometry is obviously not my forte.