Are these semicircles the same size?

The diagram shows an equilateral triangle, green and red semicircles, and four equal black circles. Wherever things look tangent, they are tangent.



Are the green and red semicircles the same size?

Let $2\ell$ be the side length of the triangle and $g$, $r$, and $b$ be the radii of the green, red, and black circle, respectively. We have the following equalities

$$\ell\sqrt{3}=2g+b(2+\sqrt{3})$$ $$(r+b)^2=\left(\ell-b\sqrt{3}\right)^2+b^2=\left(\ell-b(1+\sqrt{3})\right)^2+b^2\left(1+\sqrt{3}\right)^2.$$

Then $\ell=b\cdot 2(1+\sqrt{3})$, so

$g=b\left(2+\frac{\sqrt{3}}2\right)=b\cdot 2.866\dots>b\cdot 2.863\dots=b(\sqrt{6}+\sqrt{2}-1)=r$