import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.LinearAlgebra.AffineSpace.Midpoint import Mathlib.Geometry.Euclidean.Basic import Mathlib.Geometry.Euclidean.Triangle /-! # Bulgarian Mathematical Olympiad 1998, Problem 2 A convex quadrilateral ABCD has AD = CD and ∠DAB = ∠ABC < 90°. The line through D and the midpoint of BC intersects line AB in point E. Prove that ∠BEC = ∠DAC. (Note: The problem is valid without the assumption ∠ABC < 90°.) -/ namespace Bulgaria1998P2 open EuclideanGeometry theorem bulgaria1998_p2 (A B C D E M : EuclideanSpace ℝ (Fin 2)) (H1 : dist D A = dist D C) (H2 : ∠ D A B = ∠ A B C) (H3 : M = midpoint ℝ B C) : ∠ B E C = ∠ D A C := sorry

This problem does not yet have a complete solution.