The semiperimeter on a figure is defined as

(1) |

(2) |

(3) |

For a Triangle, the following identities hold,

(4) | |||

(5) | |||

(6) |

Now consider the above figure. Let be the Incenter of the Triangle , with , , and the tangent points of the Incircle. Extend the line with . Note that the pairs of triangles , , are congruent. Then

(7) |

Furthermore,

(8) | |||

(9) | |||

(10) |

(Dunham 1990). These equations are some of the building blocks of Heron's derivation of Heron's Formula.

**References**

Dunham, W. ``Heron's Formula for Triangular Area.'' Ch. 5 in
*Journey Through Genius: The Great Theorems of Mathematics.* New York: Wiley, pp. 113-132, 1990.

© 1996-9

1999-05-26