Triple the Area of a Circle

[Acorn]

This is possibly the last Circle Challenge as the math / maths might be getting in the way of what are supported to be accurate design approaches to laying out and scaling circles using the power of Xara.

Can you accurately, without calculation, construct a circle from another so the new circle's area is three times larger?



At present I have two construction methods but both involve some in-between scaffolding.

Good thinking,
Acorn

[Rik]

Using a similar method to your twice the area...
Does it involve drawing a hexagon at the end, and then drawing a circle within the bounds of that hexagon?

[Acorn]

Using a similar method to your twice the area...
Does it involve drawing a hexagon at the end, and then drawing a circle within the bounds of that hexagon?

Rik, I don't know how to do that so have a go. I did try with hexagons but could scale up correctly.

Hint: my present approaches use one of the following constructors: (1) a triangle, (2) two circles & (3) one circle.

Acorn

[Rik]

So, does this method work.
I'm sure you don't want me to explain how?!
I'm sure you can duplicate what I've shown!

[ss-kalm]

Rik, I just wish I could prove that mathematically, however it's beyond me! It does APPEAR to work though.

[Rik]

Rik, I just wish I could prove that mathematically, however it's beyond me! It does APPEAR to work though.

Actually, if I now check the numbers, the exercise we did where we doubled the size of the circle, it is not accurate.
I drew a circle with a radius of 30. The area = 2827.43
The radius of the larger circle comes to 42.3. This makes the area = 5621.22
That's less than it should be.

Therefore, if we allow that, then my method of making the circle three times the area is close!!!
But, not accurate.
So, I don't know what Acorn thinks about all this?