"Quite frankly, if she had said, 'I don't support it,' or 'I'm not into it,' I wouldn't have done it," Armstrong, 37, told PEOPLE at the Clinton Global Initiative on Wednesday in New York. "But Kristin has been an amazing supporter. Very flexible and just amazing with the kids. I need that from her" to do this.
Then Armstrong broke the news to his 8-year-old son, with some fear that it might leak.
"I said, 'Luke, don't tell your sisters,'" Armstrong recalls. "His sisters tell people everything. But I fully expected him to tell them."
Instead, when he talked to twin 6-year-old daughters Isabelle and Grace, he found out Luke had kept his secret. Now it was the girls' turn. "I had to tell them, 'Don't go to school and tell everybody.' When it finally came out, they said, 'Okay, NOW can we tell everybody?'"
Racing for Cancer AwarenessAfter three years of retirement – it will be four next year – Armstrong will return to the Tour de France as part of an effort to raise cancer awareness.
In mid-July, the Texas-based Livestrong organization agreed to allocate $2 million to fund a small international program.
Armstrong, a cancer survivor who had been riding in four or five charity events a year, "started training more and more seriously," he says, "and realized, 'I want to do this again.' I still love to ride my bike five hours a day, and those things coming together was a perfect storm."
With friends and family firmly in his corner, Armstrong's goals are to "change the face of the disease worldwide, to increase funding, increase education, and erase the stigma of the disease in certain cultures." He also hopes for a big turnout for the Livestrong Global Cancer Summit in Paris at the end of the Tour de France in July.
He adds, "On the racing side, I'm starting with modest expectations." As long as his other goals are met, he says, "I'll be content."
1999: Lance overcomes cancer to win Tour de France!
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