Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_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} {p q : P} {as : AffineSubspace ℝ P},
  s.IsTangentAt p as → q ∈ as → dist q s.center ^ 2 = s.radius ^ 2 + dist q p ^ 2

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

6 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor