Two equal circles of radius R are touching each other externally. If a smaller circle of radius r is touching both of these circles as well as their direct common tangent, then the ratio r:R is
Length of common tangent to circles of equal radii = 2×radius
Here l=2R
$\implies AD = DC = BE = \dfrac{1}{2} = R$
AB=R+r
AE=R−r
AB2=AE2+BE2
⟹(R+r)2=(R−r)2+R2
⟹4Rr=R2
⟹41=Rr⟹r:R=1:4