如图,AB是⊙O的直径,弦CA、BD的延长线相交于点E,EF垂直BA的延长线于点F.求证:
(1)∠DEA=∠DFA;
(2)AB2=BE•BD﹣AE•AC.
证明:(1)连接AD,因为AB为圆的直径,
所以∠ADB=90°,
又EF⊥AB,∠AFE=90°,
则A,D,E,F四点共圆
∴∠DEA=∠DFA(1分)
(2)由(1)知,BD•BE=BA•BF,
又△ABC∽△AEF∴ ABA
The fact that so many people still smoke that we need a nationwide campaign _________ the awareness of the dangers of smoking.