Affine.Simplex.dist_incenter
∀ {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) (i : Fin (n + 1)),
dist s.incenter (s.touchpoint ∅ i) = s.inradiusThe distance between the incenter and its projection in the plane of each face is the inradius.
- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
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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 · 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.touchpointstatement · cited by 49
- Affine.Simplex.incenterstatement · cited by 35
- Affine.Simplex.excenterExists_emptyproof · cited by 28
- Affine.Simplex.inradiusstatement · cited by 11
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