Droz-Farny line theorem

In a triangle, two perpendicular lines through its orthocenter meet the sides at four points whose paired segment midpoints lie on one straight line.

Orthocenter: The common intersection point of a triangle’s three altitudes. Both perpendicular lines in the theorem pass through this point.
Triangle: A polygon with three sides and three vertices. Its sides provide the lines intersected by the perpendiculars.
Arnold Droz-Farny: A Swiss mathematician associated with the theorem that bears his name. The theorem is named after him.
Acute triangle: A triangle whose three interior angles are less than 90 degrees. Its orthocenter lies inside the triangle, making the construction easy to visualize.
Altitude: A perpendicular from a vertex of a triangle to the line containing the opposite side. Altitudes define the orthocenter that anchors the two lines.
Line segment: The part of a line bounded by two endpoints. The four segments are formed by the side-intersection points.
Henri Brocard: A French mathematician known for work on triangle geometry and Brocard points. Droz-Farny’s theorem appears in the tradition of classical triangle geometry associated with Brocard.
Obtuse triangle: A triangle with one interior angle greater than 90 degrees. Its orthocenter lies outside the triangle, yet the theorem’s line relation still applies.
Midpoint: The point halfway between two endpoints of a line segment. The theorem’s collinearity concerns the midpoints of four segments.
Collinearity: The property of lying on one straight line. The theorem asserts that four constructed midpoints are collinear.