Do these segments meet? No!

Interestingly, the solution S1 is real only for k > -7/25, that is for ã < 106.26 degree, the meaning of which missing me. For each k>  -7/25 (except the case k = 0!), S1 gives the value of b < 1, and I consider here one particular case of k = , for which I write down some relevant values:
a = CB = 1,  b = AC = ,  ã = angle ACB =  ,
c = BA = ,
AD = ,
BE =
CF = ,
CD =  .
This triangle is shown here  and it is clearly seen that three segments do not meet in one point.