如图,AE是⊙O的切线,切点为A,BC∥AE,BD平分∠ABC交AE于点D,交AC于点F (1)求证:AC=AD; (2)若BC=3,FC=3/2,求AB长.

问题描述:

如图,AE是⊙O的切线,切点为A,BC∥AE,BD平分∠ABC交AE于点D,交AC于点F

(1)求证:AC=AD;
(2)若BC=

3
,FC=
3
2
,求AB长.

(1)证明:作直径AG交BC于H,∵AE是⊙O的切线,切点为A,∴AG⊥AD,∵BC∥AE,∴AG⊥BC,∵AG为直径,∴AG是BC的垂直平分线,∴AB=AC,∵BD平分∠ABC,∴∠ABD=∠DBC,∵BC∥AE,∴∠ADB=∠DBC,∴∠ABD=∠ADB,∴A...