Though this problem probably can be solved in multiple ways, one solution approach helps explain its title.
Ray AX bisects angle BAC, intersecting side BC at X
BX/XC = AB/AC
Source: Math Gazette, December 1974
Hint: Construct AB'C', the mirror image of triangle ABC in AX. Then...
Note: With the diagram arranged with point A at the top of your paper and by constructing segment CC', either a "xmas" tree or "star" shape is created by the symmetry.
Solution Commentary: The solution involves a good use of proportional relationships.
Construct segment BB' and CC'
By similar triangles BB'X and CC'X, BX/XC = BB'/C'C
By similar triangles ABB' and AC'C, BB'/C'C = AB/AC'
But, AC' = AC implies by transitivity that BX/XC = AB/AC