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Omni-MATH / In a plane, equilateral triangle ABC, square BCDE, and regular dodecagon DEFGHIJKLMNO each have side length 1 and do not overlap. Find the area of the circumcircle of △AFN.

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problem

In a plane, equilateral triangle ABCA B C, square BCDEB C D E, and regular dodecagon DEFGHIJKLMNOD E F G H I J K L M N O each have side length 1 and do not overlap. Find the area of the circumcircle of △AFN\triangle A F N.
Plain-text mathematical notation (without MathML)
In a plane, equilateral triangle ABC, square BCDE, and regular dodecagon DEFGHIJKLMNO each have side length 1 and do not overlap. Find the area of the circumcircle of △AFN.
Original LaTeX notation
In a plane, equilateral triangle $A B C$, square $B C D E$, and regular dodecagon $D E F G H I J K L M N O$ each have side length 1 and do not overlap. Find the area of the circumcircle of $\triangle A F N$.

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