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 $O B$ and $A B$, respectively. If the area of the triangle $A M N$ is $\frac { 4 } { 9 }$ of the area of the triangle $O A B$ and $\mathrm { AN } : \mathrm { NB } = \lambda : 1$, then the sum of all possible value(s) of $\lambda$ is: (1) 2 (2) $\frac { 5 } { 2 }$ (3) $\frac { 1 } { 2 }$ (4) $\frac { 13 } { 6 }$
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 $O B$ and $A B$, respectively. If the area of the triangle $A M N$ is $\frac { 4 } { 9 }$ of the area of the triangle $O A B$ and $\mathrm { AN } : \mathrm { NB } = \lambda : 1$, then the sum of all possible value(s) of $\lambda$ is:\\
(1) 2\\
(2) $\frac { 5 } { 2 }$\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 13 } { 6 }$