Theorems · Theorem · geometry

EuclideanGeometry.Sphere.dist_sq_eq_of_mem_orthRadius

∀ {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] {s : EuclideanGeometry.Sphere P} {p q : P},
  q ∈ s.orthRadius p → dist q s.center ^ 2 = dist p s.center ^ 2 + dist q p ^ 2

Alias of the reverse direction of EuclideanGeometry.Sphere.dist_sq_eq_iff_mem_orthRadius.

Defined in

Mathlib.Geometry.Euclidean.Sphere.OrthRadius

Cited by

2 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor