Double the Area of a Circle

[Acorn]

Hi Acorn, My bad, thought you were asking for help, didn't realise this was a challenge.
Many thanks, Ben

No worries Ben, some math / maths en route is no bad thing.

Acorn

[handrawn]

forgotten most of mine

[ss-kalm]

Trying to work from memory here, and you know how dangerous that is ...



Draw circle - rotate 45° - convert to editable shapes - break at points. Draw square - align to broken shapes - draw circle - stretch to align with edges of square.

[handrawn]

okay a simlpe solution - no calculation just an assumption:

make a circle 210mm wide this is your start point

align it to the bottom and sides of your page

drag it to increase size until it snaps to top of page - job done

given the assumption: your default page is A4 portrait no shadow

I guess this may be considered out-of-the-box if not disqualified in some way... but at least it follows on from what we have been saying, to which there was some point

[handrawn]

I think you are onto something there keith..

how about:

make square same width/height as circle - the circle that aligns with the four corners of this square will be the one you want:

[ss-kalm]

Clue ... Sin 45 = O/H = 0.7071 ...

Therefore radius of inner circle = 0.7071 of radius of outer circle.

[handrawn]

oh please I knoweth not the math and the signs he giveth

edit - and besides, that's a calculation and therefore going off at a tangent [but I do see what you mean, I think - we have the same square root of 2 ratio, inverted, that acorn was refering to... ? I can handle ratios; but numbers, like letters, are apt to confuse me when they get serious as someone once said ]

[Acorn]

Trying to work from memory here, and you know how dangerous that is ...



Draw circle - rotate 45° - convert to editable shapes - break at points. Draw square - align to broken shapes - draw circle - stretch to align with edges of square.

Keith, good memory.
The length of the centre of the square to a corner is √2, which must therefore be the radius of the outer circle.

Your steps are more than I would have considered but it is a working solution.

Acorn

[Acorn]

okay a simlpe solution - no calculation just an assumption:
make a circle 210mm wide this is your start point
align it to the bottom and sides of your page
drag it to increase size until it snaps to top of page - job done
given the assumption: your default page is A4 portrait no shadow
I guess this may be considered out-of-the-box if not disqualified in some way... but at least it follows on from what we have been saying, to which there was some point

handrawn, it works so it is a solution.
Thereafter you could scale both circles at the same time to any other size.
In XWD(P), you don't have an A4 template so you would have to know the Custom dimensions to enter, but as there were no "calculations" you get a pass.

Acorn

[Acorn]

I think you are onto something there keith..

how about:

make square same width/height as circle - the circle that aligns with the four corners of this square will be the one you want:

That is a good refinement of Keith's approach.

i have a wheeze / trick / gimmick that I think improves even on this.

Acorn