1. The problem statement, all variables and given/known data Given a triangle ABC with BC = 2AB. D and E are the midpoints of BC and BD respectively. Show that AD bisects angle CAE. 2. Relevant equations 3. The attempt at a solution Let AB= x, so DC= AB= x and ED = x/2. If AD bisects angle CAE, then AC/AE = DC/DE AC/AE = x/(x/2) AC: AE = 2:1 That's how far i can do... I tried using sine rule to prove that AC:AE = 2:1 but it did not help. Can anyone guide me?