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Dodexagon

In the diagram, B, A, C, D, E, F, G, H, I, J, K and L are the vertices of a regular dodecagon and B, A, M, N, O and P are the vertices of a regular hexagon.
Show that A, M and E lie on a straight line.

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If you enjoyed this puzzle, check out Sunday Afternoon Maths XXXIX,
puzzles about dodecagons, or a random puzzle.

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