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Related: Culture Forums, Support ForumsBrain work, geometry edition
With a square 48 inches, what is the largest diameter of two circles that will fit inside?
Edit to add: the circles are the same size.
yonder
(9,669 posts)That answers the question accurately I think. If the circles are to be the same size as shown, I'm thinking.
Ptah
(33,034 posts)yonder
(9,669 posts)Ptah
(33,034 posts)RockRaven
(14,989 posts)I think the diameter would be equal to 48/(1+1/√2)
ProfessorGAC
(65,138 posts)I get 28.12"
Ptah
(33,034 posts)Ptah
(33,034 posts)gratuitous
(82,849 posts)A square of 48 inches per side would yield a diagonal of 67.88 inches, which would accommodate two circles of diameter 33.94 inches.
Ptah
(33,034 posts)intrepidity
(7,331 posts)Ptah
(33,034 posts)intrepidity
(7,331 posts)yonder
(9,669 posts)to the intersection of the tangents. The diameter is going to be smaller in the neighborhood of 28 and change but Im wrestling with how to calc it.
Edit: what the OP just said.
Ptah
(33,034 posts)intrepidity
(7,331 posts)Ptah
(33,034 posts)5. If it is two identical circles, then
I think the diameter would be equal to 48/(1+1/√2)
https://www.democraticunderground.com/?com=view_post&forum=1018&pid=1803704
intrepidity
(7,331 posts)48/((2*R)+(2*R)/√2)
intrepidity
(7,331 posts)If we call the dashed line "s" then
2R + s = 48
or
s = 48 - 2R
We know that, for hypoteneus h:
h^2 = 2s^2
and
h = 2R
so
4R^2 = 2s^2
Since
s = 48 - 2R
then
4R^2 = 2(48-2R)^2
Ah, ok, now I see.
Response to Ptah (Original post)
yonder This message was self-deleted by its author.
Without using formulas, so probably wrong.
Logic is: 24 is too small, 30 is too big, so split the difference.
Jack the Greater
(601 posts)RockRaven's answer seems convincing, but I am not familiar with the math to get to it. Square root of 2 was never my forte