Consider circle, $H$, with radius $h$. A smaller circle, $F$, with radius $f$, is position such that it's curve passes through the centre of $H$ but it is not contained entirely within the circumference of $H$. Inside $F$ exists an isosceles triangle with two side lengths equaling $f$. Inscribed within this triangle is a circle, $R$, with radius $r$.
Given that $R$ must be contained entirely within the circumference of $H$, find the maximum percentage that $R$ can take up of the area of circle $H$.
(Note: The following image isn't necessarily the correct relative sizes of circles $F$ and $R$ for $R$ to have the largest possible area. This is just here to act as a visual aid)
