Bi-bisector triangle in  the 3-4-5 triangle

Coordinates of the vertices of the ABC triangle:
C{0,0}, B{3,0}, A{0,4}.
The angles CAF  and GAB are 1/4-th of the angle CAB,
the angles ABG and EBC are 1/4-th of the angle ABC,
the angles ECB and CFA are 1/4-th of the angle BCA.
CE = ,

CF = ,

AF = ,

AE = ,

BG = ,

BE =     .

Sides of the inner triangle FGE:
FG = ,
GE = ,
EF =  .

The area of the FGE triangle:



15.8028.