[King Prout]

also just guessing, but I think the white dwarf will have lost mass during its collapse phase.

as to where the centermass would be, a crude illo:

satellite>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>CM>>primary
o>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>+>>>>>O

RGcirc>>>>>>>>>>>>>>>CM>>>>>>>WD>>RGcirc
(>>>>>>>>>>>>>>>>>>>>>+>>>>>>>>>o>>>>)

[Calvin Locke]

Here are a couple of links.

Mira, x-ray photo on the page:

http://www.astronet.ru:8104/db/xware/msg/1205472


And some diagrams, including a "contact" binary. We're both right. Not sure if the enveloped companion can be
a white dwarf, but could a white dwarf strip off a red giant's gas layer to leave two white dwarfs?

http://www.astro.psu.edu/users/rbc/a1/lec16n.html