In triangle ABC, points D and E are located on sides BC and AB, respectively, with the conditions that BD equals AC, AD equals AE, and AB squared equals the product of AC and BC. The goal is to prove that the angles ∠BAD and ∠CEA are equal. The discussion involves geometric properties and relationships between the sides and angles of the triangle. Participants explore various geometric theorems and relationships to establish the proof. Ultimately, the focus is on demonstrating the angle equality through the given conditions.
