Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius
∀ {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] {n : ℕ} {r : ℝ} (s : Affine.Simplex ℝ P n) {p₁ : P},
(∀ (i : Fin (n + 1)), dist (s.points i) p₁ = r) →
↑(s.orthogonalProjectionSpan p₁) = s.circumcenter →
s.points 0 ∈ affineSpan ℝ (Set.range s.points) →
dist p₁ s.circumcenter * dist p₁ s.circumcenter = r * r - s.circumradius * s.circumradius- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- 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
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement and proof · cited by 417
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.eq_or_eq_reflection_of_dist_eqproof · cited by 0