On extriangles and excevians - Fajardo, Paul Emil D. (Animo Repository, 2009)
This thesis is an exposition of the articles Extriangles and Excevians by Larry Hoehn published in Mathematics Magazine Volume 74, Number 5, 2001 and A Geometric Proof of Heron's Formula by Shannon Umberger found in http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/MATH7200/HeronFormulaProject/GeometricProof/geoproof.htm. The first article extends some concurrency theorems of cevians of triangles to extriangles and the second gives a geometric proof of Heron's Formula. In this thesis elementary geometric proofs of the theorems stated in the articles are provided. Moreover, a geometric proof of the area formula of a triangle in terms of the lengths of its medians using the results on extriangles and excevians is discussed.