Equilateral triangles on a triangle

BAD, ACE, BCF are equilateral triangles outside a triangle ABC with one common side respectively. Prove that...[br]a) AF = CD = BE[br]b) AF, CD and BE intersect at the same point in 60[math]^\circ[/math][br]c) If X, Y, Z are the centers of triangles BAD, ACE and BCF respectively, XYZ is an equilateral triangle.

Information: Equilateral triangles on a triangle