Droz-Farny line theorem | plane geometry | advanced level

Episode 122.

Droz-Farny line theorem | plane geometry | advanced level.

Branch of mathematics: plane geometry.
Difficulty level: advanced.

Droz-Farny line theorem. Let $ABC$ be a triangle with orthocenter $H$. Let $\ell_1$ and $\ell_2$ be two perpendicular lines passing through $H$. Let $D_1$, $E_1$, $F_1$ be the intersection points of $\ell_1$ and the lines $BC$, $CA$, $AB$ respectively. Let $D_2$, $E_2$, $F_2$ be the intersection points of $\ell_2$ and the lines $BC$, $CA$, $AB$ respectively. Then the midpoints of the segments $D_1D_2$, $E_1E_2$, $F_1F_2$ are collinear.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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