import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 5
Let ABC be a triangle and P be an interior point of ABC.
Show that at least one of the angles ∠PAB, ∠PBC, ∠PCA is
less than or equal to 30°.
-/
namespace Imo1991P5
open scoped Affine EuclideanGeometry Real
theorem imo1991_p5
(A B C P : EuclideanSpace ℝ (Fin 2))
(hABC : AffineIndependent ℝ ![A, B, C])
(hP : P ∈ interior (convexHull ℝ {A, B, C})) :
∠ P A B ≤ π / 6 ∨ ∠ P B C ≤ π / 6 ∨ ∠ P C A ≤ π / 6 := sorry
end Imo1991P5
This problem does not yet have a complete formalized solution.