Theorems · Theorem · geometry

Affine.Triangle.excenter_eq_incenter_or_excenter_singleton

∀ {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) (signs : Finset (Fin 3)),
  Affine.Simplex.excenter t signs = Affine.Simplex.incenter t ∨
    ∃ i, Affine.Simplex.excenter t signs = Affine.Simplex.excenter t {i}

An excenter of a triangle is either the incenter or the excenter opposite a vertex.

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

1 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor