Peaches Geldof, the daughter of musician Bob Geldof and the late Paula Yates, died of a heroin overdose after relapsing into use of the illegal drug following attempts to give it up, an inquest heard Wednesday. The death of the 25-year-old TV host in April at her home in Wrotham, Kent, southeast of London, shocked the entertainment world. Detective Chief Inspector Paul Fotheringham of Kent police told the inquest that Geldof had been addicted to heroin for a number of years but had ceased taking the drug more recently. Geldof, who had two children younger than 2, had been supported by drug treatment workers for 2Â 1/2 years, being prescribed methadone, he said. She had said she wanted to come off methadone completely and was following a reduction plan. A drug test in November indicated that she was not taking any illegal drugs, he said. However, in February, witnesses reported suspicions that she had started using heroin again. High-grade heroin Fotheringham's report to the inquest gave new details of Geldof's death. Police who searched the house where she died found a black cloth bag hidden in a cupboard above the door of a spare bedroom, he said. Inside was a bag containing what tests proved to be heroin as well as a bag of citric acid, used to make the heroin more soluble in water for injection, according to the report. The bag also held dozens of syringes, some sealed