Given is an acute-angled triangle ABC in which holds ∣BC∣:∣AC∣=3:2. Let D be the midpoint of the side AC, and P the midpoint of the segment BD. A point X is given on the line AC so that ∣AX∣=∣BC∣, where A is between X and C. The line XP intersects the side BC at point E. The line DE intersects the line AP at point Y. Prove that the points A, X, Y, E lie on one circle if and only if ∣AB∣=∣BC∣. geometryConcyclicisosceles