The combined equation of pair of lines joining point of intersection A and B of the line L=x+y−λ=0 and the curve x2+y2−2x−4y+2=0 to the origin ' σ is
x2+y2−2(x+2y)(‌
x+y
λ
)+2(‌
x+y
λ
)2=0
Since, ‌‌∠AOB=90∘...(i) ∴ Sum of the coefficients of x2 and y2 terms is zero. ⇒(λ2−2λ+2)+λ2−4λ+2=0
⇒‌‌2λ2−6λ+4=0⇒λ2−3λ+2=0⇒λ=1,2
So, the possible equation of line L are x+y−1=0 and x+y−2=0 Therefore the required distance =‌