Theorems · Theorem · geometry

EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent

∀ {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} {as : AffineSubspace ℝ P} [Nonempty ↥as]
  [as.direction.HasOrthogonalProjection], Metric.infDist s.center ↑as = s.radius ↔ s.IsTangent as

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

0 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection