Theorems · Theorem · geometry

Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius

∀ {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] {n : ℕ} [inst_4 : NeZero n] {s : Affine.Simplex ℝ P n}
  [hf : Fact (Module.finrank ℝ V = n)] {signs : Finset (Fin (n + 1))},
  s.ExcenterExists signs →
    ∀ (i : Fin (n + 1)),
      affineSpan ℝ (Set.range (s.faceOpposite i).points) = (s.exsphere signs).orthRadius (s.touchpoint signs i)

Defined in: Mathlib.Geometry.Euclidean.Incenter
Cited by: 2 results in Mathlib
Foundations: Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace MetricSpace NormedAddTorsor NeZero Fact

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Cites28

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
Finsetstatement and proof · cited by 13,712
Submoduleproof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
InnerProductSpacestatement and proof · cited by 3,523
Factstatement and proof · cited by 2,726
Module.finrankstatement and proof · cited by 1,770
MetricSpacestatement and proof · cited by 1,684
LT.lt.ne'proof · cited by 1,417
NormedAddTorsorstatement and proof · cited by 1,325
AffineSubspacestatement · cited by 871

Cited by2

Results whose statement or proof uses this declaration.

Affine.Triangle.affineSpan_pair_eq_orthRadiusproof · cited by 1
Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphereproof · cited by 0