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9 of the same shape (Posted on 2012-07-19) Difficulty: 3 of 5
Determine whether the following construction is possible:

Dissect an equilateral triangle into 9 similar triangles with angles of 45, 60 and 75 degrees; one at each corner and the other six meeting at a point and forming a hexagon.

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

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Basic Layout | Comment 1 of 3
This layout shows vertex points  as it is too difficult to aesthetically fill in the lines.
                                    A
                                
                              u   
                                          v

                                 
                     w           o      
                                                    x

              
              B          y             z               C        

This is very close to what Jer asks but is not precise since I made a few assumptions in my drawing.

My triangle ABC has sides of 3 units. 'o' is the incentre.  Au, By and Cx are each 1 unit.  Av, Bw and Cz are approx 1.6 units.

The points u,v,w,x,y,z form the required hexagon, but not in the order given.

My plotting accuracy was set to integers (so actually my 1 unit measured 200).


Upon rereading I note the word "construction"!  :-( 

I had not attended to measuring all of my angles.  Having found a "workable construction" I posted a little later.  Therein I note some discrepancy in the above.

Edited on July 20, 2012, 10:15 pm
  Posted by brianjn on 2012-07-19 22:49:23

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