Finding distance needed to move box down in a circle so corners intersect circle edge

[pyramid]

Hi,

I'm hoping someone can help with a little problem...
I'll apologise in advance, my mathematic skills are very basic!
This is from a design perspective and I'm trying to find a mathematical way of documenting how an arc appears at the bottom of a box.

(if the following doesn't make sense, see the image below, probably easier to see what I'm trying to achieve!)

So far, I have a box (say 100 wide). The diameter of the circle the arc is formed from, is 4x the width of the box.
The circle then needs to sit at the bottom of the box where the corners of the box intersect the circle edge.
I would like to know if there is a formula, so that I can move the circle up x amount from the bottom of the box so that the edges of the circle intersect the corners of the box.
(the box and circle will always be centre aligned btw)

If it's a case of it's better to find x from the centre of the circle to the bottom of the box, then that's cool too. I'm just trying to find a formula for the positioning so that the edges of the box intersect the circle edge.

Thanks in advance!
Dave

 

[Deleted member 4993]

Hi,

I'm hoping someone can help with a little problem...
I'll apologise in advance, my mathematic skills are very basic!
This is from a design perspective and I'm trying to find a mathematical way of documenting how an arc appears at the bottom of a box.

(if the following doesn't make sense, see the image below, probably easier to see what I'm trying to achieve!)

So far, I have a box (say 100 wide). The diameter of the circle the arc is formed from, is 4x the width of the box.
The circle then needs to sit at the bottom of the box where the corners of the box intersect the circle edge.
I would like to know if there is a formula, so that I can move the circle up x amount from the bottom of the box so that the edges of the circle intersect the corners of the box.
(the box and circle will always be centre aligned btw)

If it's a case of it's better to find x from the centre of the circle to the bottom of the box, then that's cool too. I'm just trying to find a formula for the positioning so that the edges of the box intersect the circle edge.

Thanks in advance!
Dave

Use Pythagorus

(200 - x)² +50² = 200²

Solve for 'x'.

 

[pyramid]

Use Pythagorus

(200 - x)² +50² = 200²

Solve for 'x'.

Awesome!
So, I've now got:

where w is width of box...

x = (w×2) - √( (w×2)² - (w÷2)² )

Probably ugly but seems to work.
Circle radius will always be 2x width of box, so I can use just one variable.

Many thanks for your quick response!