Ok look at this image.

I'm 99% certain that this is impossible to construct as joining the bottom left corner with the top left corner creates a 20 degree angle. It also creates a essential trisection of 60 degrees, but i can't tell for sure.

The closest i have gotten to 20 degrees is 19.1.

The two trianges are equlateral.

radio
Apr 21, 2015

#5**+8 **

Start with the large equilateral triangles - they are easy to construct with straight-edge and compass. Then you can draw the larger circle easily enough - you don't need to use a 20° angle. The four smallest equilateral triangles are also easy to construct (I'm assuming the four intermediate equilateral triangles created by the intersection of the two large triangles are themselves equal in size to four of the smallest triangles.

.

Alan
Apr 23, 2015

#2**+8 **

I do not understand what you mean radio, it is already constructed on this page :/

I don't know where you want the 20 degree angle. If the 2 big triangles are equilateral then they have to be congruent because they have the same height. ???

Melody
Apr 22, 2015

#3**+5 **

I mean with a unmarked staight edge and compass, how could I contruct an accurate version or not.

radio
Apr 22, 2015

#4**+8 **

Thanks Radio

I will include your question in the wrap - maybe someone will take up your challenge :)

Does it have to be a ruler and pair of compasses?

It might be fun to try and construct it using co-ordinate geometry and Desmos graphing calculator :)

Melody
Apr 23, 2015

#5**+8 **

Best Answer

Start with the large equilateral triangles - they are easy to construct with straight-edge and compass. Then you can draw the larger circle easily enough - you don't need to use a 20° angle. The four smallest equilateral triangles are also easy to construct (I'm assuming the four intermediate equilateral triangles created by the intersection of the two large triangles are themselves equal in size to four of the smallest triangles.

.

Alan
Apr 23, 2015