Theorems · Theorem · geometry

Affine.Simplex.dist_circumcenter_eq_circumradius

∀ {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} (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
  dist (s.points i) s.circumcenter = s.circumradius

All points have distance from the circumcenter equal to the circumradius.

Defined in

Mathlib.Geometry.Euclidean.Circumcenter

Cited by

12 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor