The sides of a triangle do not meet in a point, so there is no "the common point".
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BiAngle, two lines leave from point A on a sphere and after 180 degrees they meet on point B <><><><> However, by definition, a triangle will always have THREE sides.
The point where all three angle bisectors meet is the centre of the incircle - the circle which touches all the sides of the triangle (alternatively described as the circle for which the sides of the triangle are tangents).
The radius is DE
< the point where the two rays meet is called a vertex.