问题描述：
一道美国数学竞赛题
Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.大意是说半径分别为2,4,6的三个圆
A,B,C两两相切,AB的公切线和AC的公切线相交于X,求X角的大小.大概是这样吧,本人不才.
poseidon526，你的答案好像有些不对啊，那个角怎么看都是钝角啊
Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.大意是说半径分别为2,4,6的三个圆
A,B,C两两相切,AB的公切线和AC的公切线相交于X,求X角的大小.大概是这样吧,本人不才.
poseidon526，你的答案好像有些不对啊，那个角怎么看都是钝角啊
问题解答：
我来补答
连接AB,BC,AC,AI//DE,AH//FGAB^2+AC^2=(2+4)^2+(2+6)^2=100=BC^2∴ △ABC为直角三角形.∠CAB=90sin1=BI/AB=(4-2)/(4+2)=1/3, ∠1=19.47sin2=CH/AC=(6-2)/(6+2)=1/2,∠2=30∠3=∠4=90∠5=360-∠1-∠2-∠3-∠4-∠BAC=360-19.47-30-90-90-90=40.53∠X=180-∠5=139.47度
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