It need not be - it depends on what the three lines are!
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No. The angle bisector is a line. Where the three lines meet is the median. In an equilateral triangle the INTERSECTION of the angle bisectors is the median.
orthocenter
This point "p" identifies a geometric location known, in association with each of the three "normals" which communicate with each other from their three respective vertices perpendicular to their three respective sides, as the "procedure". The normal geometric procedure of an equilateral triangle exists in a state of perfect equilibrium and divides each of the three normals in a ratio of 2:1. It is also the centre of the circle which communicates with all three vertices of the triangle, and it therefore follows that two-thirds of each normal of an equilateral triangle is a radius of the circle which contains it.
centroid
cross section