Question 20
The diagram below shows the region $R=\{(x,y)\in\mathbb R^2\mid y\ge\tfrac12x^2\}$ on the $xy$-plane bounded by the parabola $y=\tfrac12x^2$. Let $C_1$ be the largest circle lying inside $R$ with its lowest point at the origin. Let $C_2$ be the largest circle lying inside $R$ and resting on top of $C_1$. Find the sum of the radii of $C_1$ and $C_2$.
