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