Sunday, July 16, 2023

1955. A Construction For the Perspector Of 2nd Lemoine Circle

Let K=X(6)-Symmedian point of ABC. Antiparallel from K to BC intersect the AB, AC at Ac, Ab resp.
Define Ba, Bc, Ca, Cb cyclically.
KA: Antipode of K respect to circle (KBaCa). Define KB, Kcyclically.

* ABC and KAKB,KC  are perspective triangles. Perspector is X(3527) = ISOGONAL CONJUGATE OF X(631)=perspector of 2nd Lemoine circle

1987. Circumcenter On Euler Line

 Let H=X(4)-Orthocenter of ABC. A 1 B 1 C 1 cevian triangle of H. B1 A , C1 A are reflections of B1, C1 on A. L A , line through B1 A , C1...