Geometry Problem 1323: Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees

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 square (yellow); (2) D1D4D7D10 is a square (red); (3) C1C2C3C4 is a square (orange) ; (4) D1D2...D12 is a regular dodecagon (green); (5) Area B1B2B3B4 = Formula to prove; (6) Area B1B2B3B4 = 2 Area D1D4D7D10; (7) Area B1B2B3B4 = 3 Area C1C2C3C4; (8) Area D1D2...D12 = 3/4 Area B1B2B3B4.
 

Geometry Problem 1323: Square, Angle Trisector, Diagonal, Regular Dodecagon, Area


See also:
Geometry Problems
1311-1320
Visual Index
Open Problems
All Problems
Triangle
Equilateral Triangle
Square
Areas
30, 60 Angle
Angles 


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