isTangent_iff_isTangentAt_orthogonalProjection

English

s.IsTangent as if and only if s.IsTangentAt (orthogonalProjection as s.center) as.

Русский

s IsTangent как и есть и только если s.IsTangentAt(orthogonalProjection(as, s.center)) as.

LaTeX

$$$ s.IsTangent as \\iff s.IsTangentAt (orthogonalProjection as s.center) as $$$

Lean4

theorem isTangent_iff_isTangentAt_orthogonalProjection {s : Sphere P} {as : AffineSubspace ℝ P} [Nonempty as]
    [as.direction.HasOrthogonalProjection] : s.IsTangent as ↔ s.IsTangentAt (orthogonalProjection as s.center) as := by
  rw [← dist_orthogonalProjection_eq_radius_iff_isTangent, dist_orthogonalProjection_eq_radius_iff_isTangentAt]

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