Create specific shape using edges and faces

I am trying to create the blue section in this example. I am struggling to create a face representing A D P2 and P3. I have the coordinates of all the points marked there. My idea is to create the arcs P2P3, P2D, and DP3 to create a face. Do the same for the other side. But I am not sure if my topology is correct.

O1 is the center of BC. O2 is the center of AD.

I can create the upper part of the blue shape. My problem is the piece of sphere on the bottom.