2022 AMC 12A Problems/Problem 12
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Problem
Let be the midpoint of in regular tetrahedron . What is ?
Solution
Let the side length of be . Then, . By the Law of Cosines, $$ (Error compiling LaTeX. Unknown error_msg)\cos(\angle CMD) = (CM^2 + DM^2 - BC^2)/(2CMDM) = \boxed{\textbf{(B)} \, \frac13}.