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.
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1995. Circumcenter at Midpoint of BC