Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenter
∀ {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} {signs : Finset (Fin (n + 1))},
s.ExcenterExists signs →
∀ (i₁ i₂ : Fin (n + 1)),
dist (s.excenter signs) (s.touchpoint signs i₁) = dist (s.excenter signs) (s.touchpoint signs i₂)An excenter is equidistant to any two of its touchpoints.
- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.excenterstatement · cited by 63
- Affine.Simplex.ExcenterExistsstatement and proof · cited by 53
- Affine.Simplex.touchpointstatement · cited by 49
- Affine.Simplex.exradiusproof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Affine.Triangle.oangle_excenter_singleton_eq_add_piproof · cited by 1
- Affine.Simplex.dist_incenter_eq_dist_incenterproof · cited by 1
- Affine.Simplex.ExcenterExists.angle_excenter_touchpoint_eqproof · cited by 1
- Affine.Triangle.oangle_excenter_singleton_eqproof · cited by 1
- Affine.Triangle.two_zsmul_oangle_excenter_eqproof · cited by 0