Equilateral triangles on a triangle

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