∵∠ABD＝∠ABC＝∠AEC，∠BAD＝∠EAC∴△ABD∽△AEC∴AB/AE＝AD/AC∴AB·AC＝AD·AE＝AD(AD＋DE)＝AD^2＋AD·DE∵∠ADB＝∠CDE，∠ABD＝∠ABC＝∠AEC＝∠CDE∴△ABD∽△CDE∴AD/CD＝BD/DE∴AD·DE＝BD·CD∴AB·AC＝AD^2＋BD·CD
