AB是圆O的直径,AE平分角BAF交圆O于点E,过E作直线与AF垂直交AF的延长线于D,且交AB延长线于C.(1)求证:CD与圆O相切于点E.(2)若CE*DE=15/4,AD=3,求圆O的直径及角AED的正切值.
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![AB是圆O的直径,AE平分角BAF交圆O于点E,过E作直线与AF垂直交AF的延长线于D,且交AB延长线于C.(1)求证:CD与圆O相切于点E.(2)若CE*DE=15/4,AD=3,求圆O的直径及角AED的正切值.](/uploads/image/z/5199064-16-4.jpg?t=AB%E6%98%AF%E5%9C%86O%E7%9A%84%E7%9B%B4%E5%BE%84%2CAE%E5%B9%B3%E5%88%86%E8%A7%92BAF%E4%BA%A4%E5%9C%86O%E4%BA%8E%E7%82%B9E%2C%E8%BF%87E%E4%BD%9C%E7%9B%B4%E7%BA%BF%E4%B8%8EAF%E5%9E%82%E7%9B%B4%E4%BA%A4AF%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%8ED%2C%E4%B8%94%E4%BA%A4AB%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%8EC.%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9ACD%E4%B8%8E%E5%9C%86O%E7%9B%B8%E5%88%87%E4%BA%8E%E7%82%B9E.%EF%BC%882%EF%BC%89%E8%8B%A5CE%2ADE%3D15%2F4%2CAD%3D3%2C%E6%B1%82%E5%9C%86O%E7%9A%84%E7%9B%B4%E5%BE%84%E5%8F%8A%E8%A7%92AED%E7%9A%84%E6%AD%A3%E5%88%87%E5%80%BC.)
AB是圆O的直径,AE平分角BAF交圆O于点E,过E作直线与AF垂直交AF的延长线于D,且交AB延长线于C.(1)求证:CD与圆O相切于点E.(2)若CE*DE=15/4,AD=3,求圆O的直径及角AED的正切值.
AB是圆O的直径,AE平分角BAF交圆O于点E,过E作直线与AF垂直交AF的延长线于D,且交AB延长线于C.(1)求证:CD与圆O相切于点E.(2)若CE*DE=15/4,AD=3,求圆O的直径及角AED的正切值.
AB是圆O的直径,AE平分角BAF交圆O于点E,过E作直线与AF垂直交AF的延长线于D,且交AB延长线于C.(1)求证:CD与圆O相切于点E.(2)若CE*DE=15/4,AD=3,求圆O的直径及角AED的正切值.
1.AB是圆O的直径,AE平分角BAF交圆O于点E,所以角COE=角CAF,所以AF平行OE.又因为AD垂直CD,所以OE垂直CD.所以CD与圆O相切于点E.
2.角EAD=α.tanα=DE/AD,tan2α=CD/AD.又CE*DE=15/4,得tanα=1/2.所以tanAED=cotEAD=2
由上得DE=3/2,CE=5/2 .OE/AD =CE /CD,得OE=15/8, 所以圆O的直径AB=2OE=15/4
1.AB是圆O的直径,AE平分角BAF交圆O于点E,所以角COE=角CAF,所以AF平行OE。又因为AD垂直CD,所以OE垂直CD。所以CD与圆O相切于点E。
2.角EAD=α。tanα=DE/AD,tan2α=CD/AD.又CE*DE=15/4,得tanα=1/2.所以tanAED=cotEAD=2
由上得DE=3/2,CE=5/2 .OE/AD =CE /CD,得OE=15...
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1.AB是圆O的直径,AE平分角BAF交圆O于点E,所以角COE=角CAF,所以AF平行OE。又因为AD垂直CD,所以OE垂直CD。所以CD与圆O相切于点E。
2.角EAD=α。tanα=DE/AD,tan2α=CD/AD.又CE*DE=15/4,得tanα=1/2.所以tanAED=cotEAD=2
由上得DE=3/2,CE=5/2 .OE/AD =CE /CD,得OE=15/8, 所以圆O的直径AB=2OE=15/4
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