IIn a blue square A_{1}A_{2}A_{3}A_{4}
with side length 'a', the trisectors of angles A_{1}, A_{2}, A_{3}, A_{4} and
diagonals intersect at points B_{1}, B_{2}, B_{3}, B_{4}, C_{1}, C_{2}, C_{3}, C_{4}, D_{1}, D_{2}, D_{3}, ..., D_{12}
as shown in the figure.
We need to prove the following statements: (1) B_{1}B_{2}B_{3}B_{4} is a
square (yellow);
(2) D_{1}D_{4}D_{7}D_{10} is a square
(red); (3) C_{1}C_{2}C_{3}C_{4} is a square
(orange) ; (4) D_{1}D_{2}...D_{12} is a regular dodecagon
(green); (5) Area
of B_{1}B_{2}B_{3}B_{4} =
; (6)
Area of B_{1}B_{2}B_{3}B_{4} = 2 times the
area of D_{1}D_{4}D_{7}D_{10};
(7) Area B_{1}B_{2}B_{3}B_{4} = 3 times
the area of C_{1}C_{2}C_{3}C_{4};
(8) Area
D_{1}D_{2}...D_{12} = 3/4 times the area of B_{1}B_{2}B_{3}B_{4}.

Diagonals in tow,

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