On a construction of Hagge - Christopher Bradley and Geoff Smith In 1907 Hagge constructed a circle associated with each Cevian point P of triangle ABC. If P is on the circumcircle this circle degenerates to a straight line through the orthocenter which is parallel to the Wallace-Simson line of P. We give a new proof of Hagge's result by a method based on re ections. We introduce an axis associated with the construction, and (via an areal analysis) a conic which generalizes the nine-pont circle. The precise locus of the orthocenter in a Brocard porism is identifed by using Hagge's theorem as a tool. Other natural loci associated with Hagge's construction are discussed. ✪ ✪ ✪ ✪ ✪ Link tải tài liệu: LINK TẢI TÀI LIỆU Theo LTTK Education
