Assume $ABCD$ is a parallelogram. $O$ is the intersection of the diagonals and $M$ an arbitrary point in the same plan. Determine $\alpha$ for which the following relation takes place:
$\overrightarrow{MA}\cdot \overrightarrow{MC} = ||OM||^2+\alpha\cdot||AC||^2$
I drew the parallelogram and chose M outside of it. How can I write the relation to get the correct result? I'm confused. Thank you very much in advance!