∆ABC echilateral→
AB=AC=BC=x
CN=AP=BM=y
PC=AP+AC=x+y
BN=BC+CN=x+y
AM=AB+BM=x+y
↓
PC=BN=AM
∆ABC echilateral→
m(A)=m(B)=m(C)→
m(MAP)=m(PCN)=m(NBM)
Comparam triunghiurile PCN,MAP si NBM
PC=BN=AM
CN=AP=BM
m(PCN)=m(MAP)=m(NBM)
↓
triunghiurile PCN,MAP si NBM
↓
PN=MP=NM
↓
∆PNM echilateral
