“Play” the construction protocol at the bottom of this file

A triangle can be constructed if lengths of 3 sides are given.
Is there a relationship between length of one side and the sum of lengths of other two sides?

AB_1 = 5 (slider from 0 to 10, step 1)
AC_1 = 3 (slider from 0 to 7, step 1)
BC_1 = 7 (slider from 0 to 7, step 1)
A = (4.6, -1.32)
B = Point(Circle[A, AB_1])
AB = Segment(A, B)
d = Circle(A, AC_1)
e = Circle(B, BC_1)
C = Intersect(d, e, 1)
AC = Segment(A, C)
BC = Segment(C, B)