Reflections of foot of altitude of triangle with respect to sides | plane geometry | intermediate

Episode 110.

Reflections of foot of altitude of triangle with respect to sides | plane geometry | intermediate.
Reflections of the foot of an altitude of a triangle with respect to the sides | plane geometry | intermediate level.

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

Theorem. Let $ABC$ be a triangle. Let $AH_A$, $BH_B$, $CH_C$ be its altitudes. Let $P$ and $Q$ be the reflection points of $H_B$ with respect to the lines $BC$ and $AB$ respectively. Then the points $H_A$, $H_C$, $P$, $Q$ are collinear.

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

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