From The Orthic Triangle
Bill Pang
Sir Winston Churchill Secondary
Floor Location : S 209 P

The project explores various aspects of the orthic triangle - the triangle fromed by connecting the feet of altitudes of the original triangle. Through (euclidean) geometric manipulations, I found many interesting and special properties related to the orthic triangle as well as a formula relating the area of any triangle with the side lengths of its orthic triangle. Of course, during the proof I also obtained other useful results. For exmaple, I found a simple way to solve Fagnano's problem, which states that the orthic triangle is the inscribed triangle with least perimeter - another demonstration of the uniqueness of the orthic triangle. rnThe construction achieved through the derivation of my "orthic triangle theorem" offered ways to reach other well known theorems including the nine-point-circle theorem and Euler's theorem. rnThroughout the proof, I extensively used properties of centers of triangle and their associated circles.rnThe exploration of orhtic triangle has been a fruitful one.