dist_incenter — Mathlib

English

The signedInfDist from the incenter to any face has a consistent sign, yielding a fixed sign value.

Русский

ПодписанноеInfDist от инцентра к любой грани имеет единый знак.

LaTeX

$$SignType.sign (s.signedInfDist i s.incenter) = 1$$

Lean4

/-- The distance between the incenter and its projection in the plane of each face is the
inradius. -/
theorem dist_incenter (i : Fin (n + 1)) : dist s.incenter (s.touchpoint ∅ i) = s.inradius :=
  s.excenterExists_empty.dist_excenter _

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