Theorems · Theorem · geometry

EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector

∀ {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] {a b c p : P}, Sbtw ℝ a b c → p ∈ AffineSubspace.perpBisector a b → dist p b < dist p c

If p lies on the perpendicular bisector of ab and b is strictly between a and c, then p is closer to b than to c.

Defined in

Mathlib.Geometry.Euclidean.PerpBisector

Cited by

0 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor