geometry – Find 2 points (maximum distance) on a perpendicular intersecting polygon boundary

On a randomly generated convex hull, I found the 2 points of maximum distance on the perimeter of the region (the dots in black). I would like to find 2 points that are on the perpendicular to this black line, the maximum distance. (Shown in red on this image)
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I first generated a random convexhull.

points = RandomReal[{1, 3}, {np, 2}];
ch = ConvexHullMesh @ points;

Here I found the 2 points of maximum distance on the perimeter of the polygon.

maxPoints =
Quiet @ NArgMax[
    Norm[{x, y} - {u, v}], {{x, y} [Element] ch, {u, v} [Element] ch}];

My first thought would be to "sweep" perpendicular intersections along the line formed by 2 black dots, but I'm not sure how to do it.

Thank you!