Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two

∀ {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},
  p ∈ s → (s.IsTangentAt p line[ℝ, p, q] ↔ EuclideanGeometry.angle q p s.center = Real.pi / 2)

A line through p is tangent to the sphere at p if and only if the angle between the line and the radius at p equals π / 2.

Defined in

Mathlib.Geometry.Euclidean.Angle.Sphere

Cited by

0 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor