Theorems · Theorem · geometry

Affine.Triangle.orthocenter_eq_of_range_eq

∀ {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] {t₁ t₂ : Affine.Triangle ℝ P},
  Set.range t₁.points = Set.range t₂.points → t₁.orthocenter = t₂.orthocenter

Two triangles with the same points have the same orthocenter.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

1 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor