LONDON — Catherine, Princess of Wales, said in a video shared Monday that she has finished chemotherapy and is seeking to “stay cancer free,” after nine months that “have been incredibly tough for us as a family.”

       Kate, as she is widely known, is one of the most popular members of the British royal family and in line to be a future queen. The announcement will be a relief for the British monarchy, which has seen two of its most senior figures hospitalized and treated for cancer this year.