In a blue square A1A2A3A4
of side a, the trisectors of angles A1, A2, A3, A4 and
diagonals intersect at the points B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, ..., D12
as shown in the figure.
Prove that (1) B1B2B3B4 is a
(2) D1D4D7D10 is a square
(red); (3) C1C2C3C4 is a square
(orange) ; (4) D1D2...D12 is a regular dodecagon
(green); (5) Area
Area B1B2B3B4 = 2 Area D1D4D7D10;
(7) Area B1B2B3B4 = 3 Area C1C2C3C4;
D1D2...D12 = 3/4 Area B1B2B3B4.