This is book number 1938 in the Hercule Poirot Radio Dramas series.
Among the towering red cliffs of Petra, like some monstrous swollen Buddha, sat the corpse of Mrs. Boynton. A tiny puncture mark on her wrist was the only sign of the fatal injection that had killed her. With only twenty-four hours available to solve the mystery, Hercule Poirot recalled a chance remark he d overheard back in Jerusalem: You see, don t you, that she's got to be killed? Mrs. Boynton was, indeed, the most detestable woman he d ever met.
Another Christie classic which takes a series of turns that keep listeners guessing to the end. Starring John Moffatt as Hercule Poirot.