初三数学,圆的问题.你会么?⊙0的直径AB和弦CD相交于点E,已知AE=1cm,EB=5cm,∠DEB=60°,求CD的长.需要讲解和规范的步骤,讲解的越详细越好.（一个圆,AB是直径,OD垂直于AB,CD过AB交于点E,连接OF,并且OF垂直于CD） 图大概就是这样,我才一级,不能插入图片,请高手根据我所说的自己画出图形.图形倒是一点都不难画.
2019-05-27
初三数学,圆的问题.你会么?
⊙0的直径AB和弦CD相交于点E,已知AE=1cm,EB=5cm,∠DEB=60°,求CD的长.需要讲解和规范的步骤,讲解的越详细越好.（一个圆,AB是直径,OD垂直于AB,CD过AB交于点E,连接OF,并且OF垂直于CD） 图大概就是这样,我才一级,不能插入图片,请高手根据我所说的自己画出图形.图形倒是一点都不难画.
优质解答
from the question, OF垂直于CD so DF=FC consider the triangle EOF OE= 2EF
AE=1 BE=5 so OA=OB=3 OE=2 so EF=1 OF^2+EF^2=OE^2 OF^2+1=4 OF^2=3
consider the triangle DFO, OD^2=DF^2+OF^2 3^2=DF^2+ 3 DF^2=6
then we know DF, DC=2DF we can esaily get the answer.
(cannot type chinese, so sorry in the evening i can make it up)
from the question, OF垂直于CD so DF=FC consider the triangle EOF OE= 2EF
AE=1 BE=5 so OA=OB=3 OE=2 so EF=1 OF^2+EF^2=OE^2 OF^2+1=4 OF^2=3
consider the triangle DFO, OD^2=DF^2+OF^2 3^2=DF^2+ 3 DF^2=6
then we know DF, DC=2DF we can esaily get the answer.
(cannot type chinese, so sorry in the evening i can make it up)