Incenter Symmetry , Euler lines , and Schiffler Points
نویسندگان
چکیده
We look at the four-fold symmetry given by the Incenter quadrangle of a triangle, and the relation with the cirumcircle, which in this case is the nine-point conic of the quadrangle. By investigating Euler lines of Incenter triangles, we show that the classical Schiffler point extends to a set of four Schiffler points, all of which lie on the Euler line. We discover also an additional quadrangle of Incenter Euler points on the circumcircle and investigate its interesting diagonal triangle. The results are framed in purely algebraic terms, so hold over a general bilinear form. We present also a mysterious case of apparent symmetry breaking in the Incenter quadrangle.
منابع مشابه
On the Schiffler center
Suppose that ABC is a triangle in the Euclidean plane and I its incenter. Then the Euler lines of ABC, IBC, ICA, and IAB concur at a point S, the Schiffler center of ABC. In the main theorem of this paper we give a projective generalization of this result and in the final part, we construct Schiffler-like points and a lot of other related centers. Other results in connection with the Schiffler ...
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