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.

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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.

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.
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

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.

连接AB,BC,AC,

AI//DE,AH//FG

AB^2+AC^2=(2+4)^2+(2+6)^2=100=BC^2

∴  △ABC为直角三角形.∠CAB=90

sin1=BI/AB=(4-2)/(4+2)=1/3,   ∠1=19.47

sin2=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

arcsin(1/3)+2/3*pi

co

两两相切的圆之公切线有三条，不同的公切线之间的夹角是多解。

有现成的翻译所以没看英文
设A B的切点D A C的切点E
因为相切 所以∠ADX=∠AEX=90°
因为X角在四边形ADXE中 知道∠A即可解得
又三角形ABC三边分别为6 8 10
所以∠A=90°
所以X为90° 四边形ADXE是个矩形

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