Theorems · Theorem · geometry

Affine.Simplex.signedInfDist_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)),
  (s.signedInfDist i) s.incenter = s.inradius

The signed distance between the incenter and its projection in the plane of each face is the inradius. In other words, the incenter is _internally_ tangent to the faces.

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero