A generalization of the Kiepert hyperbola - Darij Grinberg and Alex Myakishev Consider an arbitrary point P in the plane of triangle ABC with cevian triangle A_1B_1C_1. Erecting similar isosceles triangles on the segments BA_1, CA_1, CB_1, AB_1, AC_1, BC_1, we get six apices. If the apices of the two isosceles triangles with bases BA_1 and CA_1 are connected by a line, and the two similar lines for B_1 and C_1 are drawn, then these three lines form a new triangle, which is perspective to triangle ABC. For fixed P and varying base angle of the isosceles triangles, the perspector draws a hyperbola. Some properties of this hyperbola are studied in the paper. ✪ ✪ ✪ ✪ ✪ Link tải tài liệu: LINK TẢI TÀI LIỆU Theo LTTK Education
