(Nearly-)Pi from Square Roots

A little something for Pi Day.
trigonograph-sqrt2+sqrt3=pi@2x

$$\begin{align}
\large \sqrt{2} + \sqrt{3} &\;=\; |\overline{AB}| + |\overline{CD}| \\[6pt]
\large &\;=\; |\widehat{AB^\prime}| + |\widehat{CD^\prime}| \\[4pt]
\large &\;\approx\; |\stackrel{\frown}{AB^\prime}| + |\stackrel{\frown}{CD^\prime}| \\[4pt]
\large &\;\approx\; |\stackrel{\frown}{AC}| \\[4pt]
\large &\;=\; \pi
\end{align}
$$