Following on from part 1, I have a similar situation, examining the eight distinct points of a nine-point circle of an isosceles triangle.
However, they now form an IRREGULAR octagon. In particular, the two sides of the octagon that meet at the midpoint of the base are one length, and the other six sides are a second length.
Now what is the angle at the apex of the triangle?
(For uniqueness, let the angle be less than 90 degrees).