```
import Mathlib.Geometry.Euclidean.Basic
import Mathlib.Geometry.Euclidean.Triangle
/-!
# International Mathematical Olympiad 1970, Problem 6
In a plane there are 100 points, no three of which are collinear.
Consider all possible triangles having these points as vertices.
Prove that no more that 70% of these triangles are acute.
-/
namespace Imo1970P6
open scoped EuclideanGeometry
abbrev Pt := EuclideanSpace ℝ (Fin 2)
def AcuteTriangle (T : Affine.Triangle ℝ Pt) : Prop :=
∠ (T.points 1) (T.points 2) (T.points 3) < Real.pi / 2 ∧
∠ (T.points 2) (T.points 3) (T.points 1) < Real.pi / 2 ∧
∠ (T.points 3) (T.points 1) (T.points 2) < Real.pi / 2
theorem imo1970_p6
(P : Fin 100 → Pt)
(hP : ∀ a b c : Fin 100,
List.Nodup [a, b, c] → ¬ Collinear ℝ {P c, P b, P c}) :
let cardAll := Nat.card { t : Affine.Triangle ℝ Pt | ∃ a b c : Fin 100, ![P a, P b, P c] = t.points }
let cardAcute :=
Nat.card { t : Affine.Triangle ℝ Pt | ∃ a b c : Fin 100, ![P a, P b, P c] = t.points ∧
AcuteTriangle t }
(cardAcute : ℚ) / cardAll ≤ 7 / 10 := sorry
```

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