1. Draw parallels to AB and AC respectively through M. The parallels divide the sides of the triangle in two equal parts. Together with the known sides of the triangle you'll get a parallelogram with one known diagonal.

2. Use Cosine rule to determine the value of the angle (see attachment)

3. Determine the value of the angle :

4. Use the Cosine rule and the angle to determine the length of BC. You should come out with