Proof

1. By propositions #5, and #6: D Incenter and E excenter

2. By proposition #8: AF=s - a and CF = s - c

3. By proposition #9: CG = s - b

4. By proposition #11 Area ABC:

5. By proposition #12 Area ABC:

6. By multiplying (4) and (5): 

7. By propositions #13, #14, #15 (Similarity AA):
   Therefore

8. Substituting in (6):
   Q.E.D.