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## Homework Statement

Given a triangle ABC with BC = 2AB. D and E are the midpoints of BC and BD respectively. Show that AD bisects angle CAE.

## Homework Equations

## 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?