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.
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 20120719 22:49:23 