On the double tangent of projective closed curves

We generalize a previous result by Fabricius-Bjerre from curves in ${\mathbb{R}}^2$ to curves in $\mathbb{R}{P}^2$. Applied to the case of real algebraic curves, this recovers the signed count of bitangents of quartics introduced by Larson-Vogt and proves its positivity, conjectured by Larson-Vogt. Our method is not specific to quartics and applies to algebraic curves of any degree.