# Computing the Triangle Maximizing the Length of Its Smallest Side Inside a Convex Polygon

• Sasanka Roy
• Soumen Nandi
• Subhas C. Nandy
• Suchismita Roy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)

## Abstract

Given a convex polygon with n vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must be common with a vertex of the polygon. Next we propose an $$O(n^2\log n)$$ time algorithm to compute such a triangle inside the given convex polygon.

## Keywords

Computational geometry Algorithms Properties of isosceles and equilateral triangles Optimal inclusion problem

## Notes

### Acknowledgement

We thank Prof. Joseph O’Rourke for valuable suggestion on the Proof of Lemma 2.

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© Springer International Publishing AG 2017

## Authors and Affiliations

• 1
Email author
• Sasanka Roy
• 2
• Soumen Nandi
• 2
• Subhas C. Nandy
• 2
• Suchismita Roy
• 1
1. 1.Department of CSENational Institute of Technology DurgapurDurgapurIndia
2. 2.Indian Statistical InstituteKolkataIndia