A bisector of a line segment connecting two points on a circle always goes through the center of the circle.
My comment was regarding the length of n1 and n2, not their direction. The illustration implies that the lengths of n1 and n2 are each equal to the distance between the respective midpoints and the center of the circle. E.g., ||n1|| == ||m1 - C||. If that were true (which I believe it is not), then finding the center would be trivial.
I'm just commenting that the illustration is misleading in that regard. Showing shorter vectors n1 and n2 (i.e., an unknown distance between the vectors heads and the center) would better highlight the need for the parameterized bisectors. Something like the following:
Ah, I see what you're talking about now.
You are right. n1 and n2 should not have the exact distance from the midpoint to the center of the circle C.
The figure is kind of misleading.