Theorems · Theorem · geometry

Affine.Simplex.eq_circumradius_of_dist_eq

∀ {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) {p : P},
  p ∈ affineSpan ℝ (Set.range s.points) → ∀ {r : ℝ}, (∀ (i : Fin (n + 1)), dist (s.points i) p = r) → r = s.circumradius

Given a point in the affine span from which all the points are equidistant, that distance is the circumradius.

Defined in

Mathlib.Geometry.Euclidean.Circumcenter

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor