What is the value of $L$ and the arcs $AG$ and $BH$?

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What is the value of $L$ and the arcs $AG$ and $BH$, as a function of $d, R$ and $r$? Note that $G, H, C, D$ are collinear and $AB$ tangent to both circles. Illustration of the problem

The problem was inspired by a question from the ACT exam.

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Hint: Please draw a line from center $C$ to line $AD$, parallel to $AB$. It will be perpendicular to line $AD$.