<p>According to <a href="https://arxiv.org/abs/1705.11035" rel="noreferrer">this</a> paper, there is a class of convex polygons in which the algorithm cited by ShreevatsaR's answer fails. The paper also proposes a O(n log n) divide and conquer algorithm for solving the problem.</p>

<p>Apparently, the simpler O(n<sup>2</sup>) algorithm in which you move points B and C for <strong>all</strong> A is still valid.</p>
How to find largest triangle in convex hull aside from brute force search
<p>Given a convex polygon, how do I find the 3 points that define a triangle with the greatest area.  </p>

<p><strong>Related:</strong> Is it true that the circumcircle of that triangle would also define the minimum bounding circle of the polygon? </p>