∀ {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.IsTangent as