Select the most distant vertex from polygon's centroid using ArcPy

I have a polygon and the polygon's centroid. I want to select the most distant vertex from centroid (picture: point A). I used arcpy.FeatureVerticesToPoints_management to create a feature class containing points generated from polygon, but I don't know what to do next. Could you help me?

Also I want to find intersection point (point B) of the outline of polygon and line created by centroid and the most distant point (line OA).

I would be very grateful for any help.

Answer

Here's a pared down version of @crmackey's answer. The polygon layer is called 'POLY1', and should be the only thing you need to change to get an output point file of farthest vertices - it creates centroids on-the-fly:

>>> points = []
>>> with arcpy.da.SearchCursor("POLY1",['SHAPE@']) as cursor:
...     for row in cursor:
...         centroid = row[0].centroid
...         dist = 0
...         for part in row[0]:

...             for pnt in part:
...                 cent_vert_dist = arcpy.PointGeometry(pnt).distanceTo(centroid)
...                 if cent_vert_dist > dist:
...                     dist = cent_vert_dist   
...                     far_point = arcpy.PointGeometry(pnt)
...         points.append(far_point)
...         
>>> arcpy.CopyFeatures_management(points,'in_memory\points')

Back-tracking to the intersection point opposite the farthest vertex is possible, but will require some additional trigonometry that I'm not prepared to get into, atm.