Mathematics - Straight Lines Question with Solution | TestHub

Let the line $x+y=1$ meet the axes of $x$ and $y$ at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB , where O is the origin and the points M and N lie on the lines $OB$ and $AB$, respectively. If the area of the triangle $AMN$ is $\frac{4}{9}$ of the area of the triangle $OAB$ and AN : NB $=\lambda :1$, then the sum of all possible value(s) of is $\lambda$ :