Affine.Simplex.ExcenterExists.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 → ∀ (i : Fin (n + 1)), dist (s.excenter signs) (s.touchpoint signs i) = s.exradius signsThe distance between the excenter and its projection in the plane of each face is the exradius.
- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- Finset.sumproof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- Finset.sum_congrproof · cited by 2,323
- absproof · cited by 1,814
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
Cited by6
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenterproof · cited by 5
- Affine.Simplex.ExcenterExists.isTangentAt_touchpointproof · cited by 5
- Affine.Simplex.ExcenterExists.touchpoint_injectiveproof · cited by 4
- Affine.Simplex.ExcenterExists.touchpoint_mem_exsphereproof · cited by 2
- Affine.Simplex.dist_incenterproof · cited by 0