A certain triangle ABC can be divided into 5 triangles each similar to ABC.
What are the angles A,B,C and how is the triangle divided?

A 30-30-120 triangle can be divided into 5 smaller similar triangles as follows: Let BC be the long side.  Trisect BC with points D and E.  This yields obtuse triangles ABD and ACE similar to ABC and an equilateral triangle ADE.  Let F be the center of the equilateral triangle. Then ADF, AEF, and DEF are all obtuse triangles similar to ABC.

Posted by Brian Smith on 2011-09-06 14:30:24