Theorems · Theorem · geometry

EuclideanGeometry.Sphere.secondInter_dist

∀ {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 : P) (v : V),
  dist (s.secondInter p v) s.center = dist p s.center

The distance between secondInter and the center equals the distance between the original point and the center.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor