Theorems · Theorem · geometry

EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt

∀ {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} [inst_4 : Nonempty ↥as]
  [inst_5 : as.direction.HasOrthogonalProjection],
  dist s.center ↑((EuclideanGeometry.orthogonalProjection as) s.center) = s.radius ↔
    s.IsTangentAt (↑((EuclideanGeometry.orthogonalProjection as) s.center)) as

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

3 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection