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If triangle ABC has sides a, b, c and semiperimeter then area of triangle ABC

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

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

By proposition #9: CG = s - b

By proposition #11 Area ABC:

By proposition #12 Area ABC:

By multiplying (4) and (5):

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

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

Last updated: February 14, 2007