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Question Number 185893 by mr W last updated on 29/Jan/23

Commented by mr W last updated on 29/Jan/23

length of common tangent line x=?

lengthofcommontangentlinex=?

Commented by som(math1967) last updated on 29/Jan/23

x=(√7) ?

x=7?

Commented by mr W last updated on 29/Jan/23

yes, thanks!

yes,thanks!

Answered by a.lgnaoui last updated on 29/Jan/23

Answered by som(math1967) last updated on 29/Jan/23

Commented by som(math1967) last updated on 29/Jan/23

AB=diagonal of square  =dist between two centre=4(√2)  BC=2+3=5  ∴AC=DE=x=(√((4(√2))^2 −5^2 ))=(√7)

AB=diagonalofsquare=distbetweentwocentre=42BC=2+3=5AC=DE=x=(42)252=7

Answered by a.lgnaoui last updated on 29/Jan/23

Triangle AEF rectangle en E  EF^2 =AF^2 − 4  Truangke DFE rectangle en F  EF^2 =DE^2 −9  AD^2 =AE^2 +DE^2 −AE×DEcos ((π/2)+α)(i)  (4(√2) )^2 =4+DE^2 +4DEsin α  △EFD      EF=(3/(tan α))  sin α=(3/(DE))     DE^2 =9+EF^2   (i)  ⇒32=4+9+EF^2 +4(3/(sin α))sin α              32=25+EF^2                   EF=(√7)

TriangleAEFrectangleenEEF2=AF24TruangkeDFErectangleenFEF2=DE29AD2=AE2+DE2AE×DEcos(π2+α)(i)(42)2=4+DE2+4DEsinαEFDEF=3tanαsinα=3DEDE2=9+EF2(i)32=4+9+EF2+43sinαsinα32=25+EF2EF=7

Answered by ajfour last updated on 29/Jan/23

Commented by mr W last updated on 29/Jan/23

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