Problem 4 (2018 AIME I)
AIME IMedium
From module Law of Cosines
Problem
In triangle ABC, AB = 6, AC = 8, and BC = 10. Point D lies strictly between A and B on AB and point E lies strictly between A and C on AC so that AD = AE and BE = CD. Then AD can be expressed in the form m/n, where m and n are relatively prime positive integers. Find m + n.