Theorems · Theorem · geometry

EuclideanGeometry.Sphere.secondInter_collinear

∀ {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' : P),
  Collinear ℝ {p, p', s.secondInter p (p' -ᵥ p)}

If the vector passed to secondInter is given by a subtraction involving the point in secondInter, the three points are collinear.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor