圆01与圆O2交与A,B,O1在圆O2上,AC不是圆O1直径,CB的延长线交与圆O2于D,求证：O1D垂直AC

圆01与圆O2交与A,B,O1在圆O2上,AC不是圆O1直径,CB的延长线交与圆O2于D,求证：O1D垂直AC
圆01与圆O2交与A,B,O1在圆O2上,AC不是圆O1直径,CB的延长线交与圆O2于D,求证：O1D垂直AC

圆01与圆O2交与A,B,O1在圆O2上,AC不是圆O1直径,CB的延长线交与圆O2于D,求证：O1D垂直AC
设O1D与AC交于Q.
则角OAC=(180-角AOC)/2
=(180-2角ABC)/2 (圆周角是圆心角一半)
=90-角ABC
=90-(180-角ABD)=角ABD-90
=角AO1D-90 (对同弧的圆周角相等)
所以 角AQO1=角AO1D-角OAC=90
证毕