Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangentAt.dist_eq_of_mem_of_mem

∀ {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} {p₁ p₂ q : P} {as₁ as₂ : AffineSubspace ℝ P},
  s.IsTangentAt p₁ as₁ → s.IsTangentAt p₂ as₂ → q ∈ as₁ → q ∈ as₂ → dist q p₁ = dist q p₂

If two tangent lines to a sphere pass through the same point q, then the distances from q to the tangent points are equal.

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

0 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor