  A graph is outerplanar if it has a planar drawing for which all vertices
belong to the outer face of the drawing. Let $H$ be a graph. The outerplanar
Tur\'an number of $H$, denoted by $ex_\mathcal{OP}(n,H)$, is the maximum number
of edges in an $n$-vertex outerplanar graph which does not contain $H$ as a
subgraph. In 2021, L. Fang et al. determined the outerplanar Tur\'an number of
cycles and paths. In this paper, we use techniques of dual graph to give a
shorter proof for the sharp upperbound of $ex_\mathcal{OP}(n,C_k)\leq \frac{(2k
- 5)(kn - k - 1)}{k^2 - 2k - 1}$.
