What is the Diameter of the outer Circle formed by 3-inner circles which Thicknes-wide is 1.25 mts? see dranw. Thank you

Question

What is the Diameter of the outer Circle formed by 3-inner circles which Thickness-wide is 1.25 mts? see drawn. Thank you

Answer 1

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