如图,点A,B,C,D在圆O上,AB=AC,AD与BC相交于点E,AE=ED/2,延长DB到点F,使FB=BD/2,连接AF判断直线AF

问题描述:

如图,点A,B,C,D在圆O上,AB=AC,AD与BC相交于点E,AE=ED/2,延长DB到点F,使FB=BD/2,连接AF判断直线AF

判断直线AF是圆O的切线吗?恩恩∵DE/DA=DB/DF=2/3∴BE∥AE,即BC∥AE∴∠FAB=∠ABC∵AB=AC∴∠ABC=∠ACB∴∠FAB=∠ACB∴FA是圆O的切线(弦切角等于该弦所对圆周角)