WRAPUP 9-Colombia rescues Betancourt, 3 US hostages

* Betancourt, 3 Americans, 11 other hostages rescued

* Military infiltrated, tricked guerrillas

* U.S. ex-hostages land in United States

By Hugh Bronstein

BOGOTA, July 2 (Reuters) - Colombian politician Ingrid Betancourt and three U.S. hostages held for years by guerrillas were rescued on Wednesday after soldiers posing as aid workers duped their captors into putting them on a helicopter.

The rescue -- without a shot being fired -- was a huge blow to Latin America's oldest insurgency, already badly weakened by President Alvaro Uribe's U.S.-backed campaign to defeat the rebels and the cocaine trade fueling Colombia's conflict.

Betancourt, 46, a dual French-Colombian citizen and former presidential candidate, was the highest-profile captive held by the Revolutionary Armed Forces of Colombia, known as FARC, and had been a held in the Colombian jungle for six years.

"I believe that this is a sign of peace for Colombia, that we can find peace," Betancourt said, weeping as she thanked the Colombian military in her first public comments, carried on Colombian radio station Caracol.

Minutes later, a pale but smiling Betancourt landed at Bogota's air force base, walking down the stairs of the plane and hugging her mother, Yolanda Pulecio, on the runway.