Radici was born as the son of the wealthy and influential Bergamo entrepreneur Gianni Radici . At the age of three he lost vision in his left eye due to glaucoma . Despite this restriction of his field of vision, which became a handicap, especially in diffuse lighting conditions, he developed into one of the best slalom riders in the world. Together with his teammates Gustav Thöni and Piero Gros , he was one of the few skiers in the mid-1970s who was able to break the dominance of Sweden's Ingemar Stenmark in slalom races.
Radici's streak of success began in December 1973 when he was able to place in the top ten for the first time in the giant slalom in Val-d'Isère . As a result, he remained consistently in the top group, especially in slalom. Between December 1973 and January 1978 he reached the top ten 29 times in World Cup races. He celebrated his greatest success by winning the slalom races in Garmisch-Partenkirchen in January 1976 and in Madonna di Campiglio ( 3-tre races ) in December 1976. In his only Olympic participation in Innsbruck in 1976 , he was eliminated as one of the favorites in slalom. In the giant slalom he reached seventh place. He also did not finish in his two world championship starts in slalom in 1974 and 1978 .
After retiring from the national ski team, Radici took over the successful management of his parents' textile company and led it to an annual turnover of 1.5 billion euros (2000). On the evening of April 14, 2002, he was found dead in a wooden shed not far from his home. He had shot himself in the head with a pistol. Radici was married to the former ski racer Elena Matous . Together the couple had a son and a daughter.