∵∠OBA＝∠OCA,且∠OAB＝∠OCB,又∵∠OBA＝∠OAB,∴∠OBA＝∠OCB,∵∠BOC＝∠BOC,∴△OBD∽△OCB（A.A.),∴r/OC＝BD/BC,∴r×BC＝OC×BD,同理,∵△OAD∽△OCA,∴AD×OC＝AC×r,两式相加：（AD＋BD）÷r＝（AC＋BC）...