, 36, died of brain cancer early Sunday in Terre Haute, Ind.
Cook announced his brother's death Sunday morning at the Race for Hope 5K in Washington, D.C. The audience responded in gasps of shock.
"I actually lost my brother yesterday to a brain tumor and I couldn't imagine being anywhere else right now," Cook told the crowd at the benefit for brain cancer research.
Cook was both the event's grand marshal and running with a team that – as of last month – had raised more than $40,000.
"I lost one today," he told the crowd of runners and supporters, "but I gained 9,000 and I will be here every year that they will have me."
A family friend told Radaronline.com that Adam died at 1 a.m. Sunday morning at a hospice in Terre Haute, though reports later in the day suggested that Cook died at home where hospice nurses were helping his wife, Kendra, care for him.
"Adam passed away peacefully," the friend said. "He was surrounded by his family, including his wife, Kendra, his children, his father and his stepmom, among others.”
Cook, a Blue Springs native, was on his way on a jet when his brother died.
"The family thought that Adam would go much sooner than this, actually," said the Cook family friend. “That’s why David left his tour a few weeks back so that he could be with Adam. They said their goodbyes then.”
Cook family friend Julie Henricks said Adam Cook had decided to stop his chemotherapy treatments early this year after they failed to help his advanced brain cancer.
"He was so sick and so worn out he just made that decision. That was his choice. It was because he was just so tired," said Henricks.
Adam is the eldest of Cook's brothers. A younger sibling, Andrew, also tried out for "American Idol" but didn't make it to Hollywood.
Watch Cook's announcement today at the Washington race here.