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After not being drafted out of Auburn University in 1997, Burke became the first Irish-born player in NBA history when he signed a contract with the Orlando Magic in 2002.
He played in 62 games with them, averaging 4.3 points and 2.4 rebounds per game. He did not play in the NBA during the 2003–04 NBA season, or the 2004–05 NBA season. In his return to the NBA, he played for the Phoenix Suns for two seasons. He was also in training camp with the Golden State Warriors in 2007 before being released.
In November 2007, Burke signed with Russian club Khimki and helped the team win their first Russian Cup title. Burke averaged 8.2 points and 5.2 rebounds per game in 211 career games played over all of the different European leagues that he competed in. In 2008, he moved to the Polish club Asseco Prokom Sopot and he helped the team to win the league's title.