A closed regular planar curve of constant width - finding an expression for the opposite point to $\alpha(s)$
HINT: Use what it means for $\beta(s)$ to be the point opposite to $\alpha(s)$. What does this tell you about $\beta'(s)$? Now calculate.
HINT: Use what it means for $\beta(s)$ to be the point opposite to $\alpha(s)$. What does this tell you about $\beta'(s)$? Now calculate.