If paying the activation cost of the ability includes sacrificing Rings of Brighthearth, the ability won't be copied. At the time the ability is considered activated (after all costs are paid), Rings of Brighthearth is no longer on the battlefield.
Rings of Brighthearth
The triggered ability of Rings of Brighthearth and the copy it creates both resolve before the ability that caused it to trigger. They resolve even if that ability is countered.
You can't pay {2} more than once for each time the triggered ability of Rings of Brighthearth resolves.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Howard Lyon
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
