Affine.Triangle.dist_orthocenter_reflection_circumcenter
∀ {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 t.orthocenter
((EuclideanGeometry.reflection (affineSpan ℝ (t.points '' {i₁, i₂}))) (Affine.Simplex.circumcenter t)) =
Affine.Simplex.circumradius tThe distance from the orthocenter to the reflection of the circumcenter in a side equals the circumradius.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites61
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommMonoidproof · cited by 12,281
- Submodulestatement · cited by 7,192
- Set.imagestatement · cited by 5,609
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
Cited by3
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_circumcenter_reflection_orthocenterproof · cited by 1
- Affine.Triangle.dist_orthocenter_reflection_circumcenter_finsetproof · cited by 0