Mathematics - Properties of Triangle Question with Solution | TestHub

Centers of both circles lie on the angle-A bisector. Their distances from A are $\sqrt{2r}$ and $\sqrt{2}$ρ. External tangency (small circle nearer A) gives $\sqrt{2}$(r-ρ)=r+ρ, so ρ/r=($\sqrt{2}$-1)/($\sqrt{2}$+1)=3-2$\sqrt{2}$.