Showing posts with label Symmedian point. Show all posts
Showing posts with label Symmedian point. Show all posts

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

Sunday, June 26, 2022

1875. Same Centers

 1. ) Let $H$ and $N_a$ be the orthocenter and Nagel's point of $ABC$. Let $X,Y,Z$ be the projections of $N_a$ on $HA, HB, HC$.

$ABC$ and $XYZ$ have same incenter.

2.) Let $K$ be the symmedian point of $ABC$. Let $X,Y,Z$ be the projections of $K$ on perpendicular bisectors of $BC, CA, AB$
** $ABC$ and $XYZ$ have same centroid.

1996. A Collinearity