Affine.Triangle.dist_circumcenter_reflection_orthocenter
∀ {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] (t : Affine.Triangle ℝ P) {i₁ i₂ : Fin 3},
i₁ ≠ i₂ →
dist (Affine.Simplex.circumcenter t)
((EuclideanGeometry.reflection (affineSpan ℝ (t.points '' {i₁, i₂}))) t.orthocenter) =
Affine.Simplex.circumradius tThe distance from the circumcenter to the reflection of the orthocenter in a side equals the circumradius.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- affineSpanstatement and proof · cited by 417
- Affine.Simplex.pointsstatement and proof · cited by 391
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_circumcenter_reflection_orthocenter_finsetproof · cited by 0