IIn a blue square A1A2A3A4
with side length 'a', the trisectors of angles A1, A2, A3, A4 and
diagonals intersect at points B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, ..., D12
as shown in the figure.
We need to prove the following statements: (1) B1B2B3B4 is a
square (yellow);
(2) D1D4D7D10 is a square
(red); (3) C1C2C3C4 is a square
(orange) ; (4) D1D2...D12 is a regular dodecagon
(green); (5) Area
of B1B2B3B4 =
; (6)
Area of B1B2B3B4 = 2 times the
area of D1D4D7D10;
(7) Area B1B2B3B4 = 3 times
the area of C1C2C3C4;
(8) Area
D1D2...D12 = 3/4 times the area of B1B2B3B4.
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