Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset
∀ {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, variant using a Finset.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- 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 and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- affineSpanstatement and proof · cited by 417
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