Are you familiar with the game Risk? The old pieces for the denomination of one army had three lines intersecting with smoothed intersections such as the ones in this picture.

Now, the cross section of these pieces, excluding the curvature, can represent your bisectors. Choosing a point x on any of those lines, and letting it be on the triangle makes this a simple problem. However, the triangle XYZ denotes a triangle formed my drawing lines from X to Y, Y to Z and Z to X. Therefore, X is treated as a vertex of the triangle. The bisector is the line that lies on the point exactly in the middle of two vertices. Therefore, to make this situation valid, the point X should lie in the center of the bisectors/risk-army/triangle effectively making the triangle non-existent because it has an absolute area of zero.