如图,在△ABC中,角C=90°,AC=4,BC=3,圆O1内切于△ABC,圆O2切BC,且与AB、AC的延长线都相切,圆O1的半径R1,圆O2的半径R2,则R1/R2等于( )?

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如图,在△ABC中,角C=90°,AC=4,BC=3,圆O1内切于△ABC,圆O2切BC,且与AB、AC的延长线都相切,圆O1的半径R1,圆O2的半径R2,则R1/R2等于(       )?
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如图,在△ABC中,角C=90°,AC=4,BC=3,圆O1内切于△ABC,圆O2切BC,且与AB、AC的延长线都相切,圆O1的半径R1,圆O2的半径R2,则R1/R2等于( )?
如图,在△ABC中,角C=90°,AC=4,BC=3,圆O1内切于△ABC,圆O2切BC,且与AB、AC的延长线都相切,圆O1的半径R1,圆O2的半径R2,则R1/R2等于( )?

如图,在△ABC中,角C=90°,AC=4,BC=3,圆O1内切于△ABC,圆O2切BC,且与AB、AC的延长线都相切,圆O1的半径R1,圆O2的半径R2,则R1/R2等于( )?
0.5

1;2

圆心和切点相连,A点和两个圆心相连,先求小圆半径,再求大圆半径,利用三角函数即可

0.5

r1=1
r2=12/7
R1/R2=7/12
O1到ac为X,则ac-X=AB-{BC-X}
X=1
O2到ac为y
3-Y=Y*3/4
(3/4为∠BAC的tg值)
y=12/7
则O1/O2=X/Y=1/(12/7)=7/12