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题型:解答题 题类:常考题 难易度:普通
已知:如图,BC是半圆O的直径,D,E是半圆O上两点,= , CE的延长线与BD的延长线交于点A.
(1)求证:AE=DE;
(2)若E=2 , tan= , 求CD.
如图所示,已知ΘO1和ΘO2相交于A,B两点.过点A作ΘO1的切线交ΘO2于点C,过点B作两圆的割线,分别交ΘO1 , ΘO2于点D,E,DE与AC相交于点P,
(Ⅰ)求证:PE•AD=PD•CE;
(Ⅱ)若AD是ΘO2的切线,且PA=6,PC=2,BD=9,求AD的长.
(Ⅰ)求证:BC•CD=AD•DB;
(Ⅱ)若BE=4,点N在线段BE上移动,∠ONF=90°,NF与⊙O相交于点F,求NF的最小值.
(Ⅰ)若∠BCM=30°,求∠ABC;
(Ⅱ)已知E为线段AB上一点,满足AE=3BE,CE⊥AB,求证:BC:AE=2:3.
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