Question Number 104157 by ajfour last updated on 19/Jul/20

Commented byajfour last updated on 19/Jul/20

Find  radii R and r of bigger and  small circles.

Answered by mr W last updated on 19/Jul/20

H(1,1)  OH=(√2)R+R=(√2)  ⇒R=((√2)/((√2)+1))=2−(√2)  D(R+2(√(Rr)),r)=(h,r)  F(k,(1/k))  tan θ=(1/k^2 )  k=h+r sin θ=R+2(√(Rr))+r (1/(√(1+k^4 )))  (1/k)=r+r cos θ=r(1+(k^2 /(√(1+k^4 ))))  ⇒r=(1/(k(1+(k^2 /(√(1+k^4 ))))))  k=R+2(√(R/(k(1+(k^2 /(√(1+k^4 )))))))+(1/(k((√(1+k^4 ))+k^2 )))  ⇒k≈1.5831  ⇒r≈0.3275

Commented bymr W last updated on 19/Jul/20

Commented byajfour last updated on 19/Jul/20

I too think, this as the possible way,  Sir, thanks for the solution!

Answered by ajfour last updated on 21/Jul/20

Commented byajfour last updated on 22/Jul/20

R=2−(√2)  C(0,R(√2))   let  y−x=s  ,  y+x=t  ⇒  y=((s+t)/2)  ,  (1/x) = (2/(t−s))  y=(1/x)    is   t^2 −s^2  = 4  s=(√(t^2 −4))   A((R/(√2))+(√(2Rr)) , (R/(√2))+(√(2Rr)) )  D((R/(√2))+(√(2Rr))−(r/(√2)) , (R/(√2))+(√(2Rr))+(r/(√2)))    .....