Wash and drain cranberries. In a heavy saucepan mix cranberries, sugar, water, cinnamon stick, apples, and grated peel of lemon and tangerines. Bring to a boil while stirring occasionally. Reduce heat and simmer for 5-7 minutes. Cranberry skins should pop and apples should turn transparent. Cool and transfer mixture to a bowl. Stir in segmented tangerines. Chill thoroughly. Remove cinnamon stick before serving.