The obturator artery supplies which compartment?

If a large collection of fluid was located posterior to the uterus and anterior to the rectum on ultrasound, which recess/pouch is it likely to be located within?

Peritoneal reflections in the pelvis are named for their relations to surrounding structures, however the ‘Pouch of Douglas’ is an eponymous name for one peritoneal reflection that is frequently used by clinicians. Between which two structures is the Pouch of Douglas?

Is this structure labelled A or B on the below CT axial image?

Why is this significant and what could be the underlying cause?