AMC 12A 2022 (Problem 12)

Let MM be the midpoint of AB\overline{AB} in regular tetrahedron ABCDABCD. What is cos(CMD)\cos(\angle CMD)?
(A)  14\text{(A)}\;\frac14(B)  13\text{(B)}\;\frac13(C)  25\text{(C)}\;\frac25(D)  12\text{(D)}\;\frac12(E)  32\text{(E)}\;\frac{\sqrt3}{2}