What is the Diameter of the outer Circle formed by 3-inner circles which Thickness-wide is 1.25 mts? see drawn. Thank you
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Is the bottom right circle supposed to touch the outer circle? – Epiousios Oct 04 '17 at 18:08
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What does this have to do with circulant matrices? – amd Oct 04 '17 at 19:42
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The height of the equilateral triangle whose side is $2r$ is $\sqrt{4r^2-r^2}=r\sqrt{3}$
$r+r\sqrt{3}+r=1.25$
$(2+\sqrt{3})r=1.25\to r=\dfrac{1.25}{2+\sqrt{3}}\approx 0.335$m
The slant red segment inside the triangle can be found using Pythagoras theorem as the small triangle has one leg that is $r$ and the other one that is $h/3=\dfrac{r\sqrt 3}{3}\approx 0.193376.$
So the length of the slant red line segment in the triangle is $\sqrt{0.335^2+0.193376^2}\approx 0.3868$m
Finally the radius of the red circle is $0.3868+0.335=0.7218$m and diameter is $1.4436$m
Hope this helps
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How do we know that one leg of the triangle inside the triangle is $h/3$? – Epiousios Oct 04 '17 at 19:09
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@Epiousios It is a property of the centroid of any triangle: the segment joining centroid with midpoint is one third of the whole median segment. https://en.wikipedia.org/wiki/Median_(geometry)#Relation_to_center_of_mass – Raffaele Oct 04 '17 at 19:14