Theorems · Theorem · geometry

Affine.Triangle.affineSpan_orthocenter_point_le_altitude

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] (t : Affine.Triangle ℝ P) (i : Fin 3),
  line[ℝ, t.orthocenter, t.points i] ≤ Affine.Simplex.altitude t i

The affine span of the orthocenter and a vertex is contained in the altitude.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

1 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor