Vancouver, British Columbia -- When Alexandra Zaretsky takes to the ice in Olympic ice-dancing competition Friday, she'll look deep into her partner's eyes as they skate the "Tango Romantica."

But not too deep. That's because her partner is her brother, 26-year-old Roman Zaretsky. "We try to find ways to kind of look through—or look a little up, or a little sideways," says Ms. Zaretsky. "Hey, you gotta act."

They're...