I discovered one Nexus of Morley triangle and equilateral triangle on the bisector following:
MNP is an equilater triangle on bisector of a triangle ABC, M1N1P1 is symmetric with MNP through I(incircle). A1,A2,A3,A4,A5,A6 are midpoints of MP1,P1N,NM1,M1P,PN1,N1M.
M2,N2,P2 are midpoints of A1A2,A3A4,A5A6. D,E,F are midpoint of M2P2,M2N2,N2P2.
=> DEF is the Morley equileteral triangle
Reference:
http://diendantoanho...c-của-tam-giác/