1. Draw a sketch.
2. Inflect the triangle ABC over the point D (not sure if this is the correct expression; see attachment)
3. You'll get a parallelogram ABA'C. The diagonal of the parallelogram is 2*(AD)
4. Consider the triangle ABA' with BA' = AC
5. According to the triangle inequality
AB + BA' > AA' = 2*(AD)
AB + AC > 2*(AD)