Approximation Approach to Holditch's Theorem

Due to recent results by the authors, Holditch's original proof of his eponymous theorem is effective when applied to a sufficiently smooth convex curve with positive curvature, since such curves were shown to possess a smooth envelope generated by a traveling chord. In the present work, we smoothly approximate a convex curve satisfying only a mild local obtuseness condition, and thereby derive Holditch's theorem for such curves without requiring them to possess an envelope.