Official solution
Equation of chord of contact is
x.0 + y.0 -- 4(x + 0) --2(y + 0) + 16 = 0
\[ \Rightarrow \] 2x + y -- 8 = 0
\[ \therefore \] Length of CM = \[\left[ {{{2.4 + 2 - 8} \over {\sqrt {{2^2} + {1^2}} }}} \right]\] = \[{2 \over {\sqrt 5 }}\] units
\[ \therefore \] AM = BM = \[\sqrt {4 - {4 \over 5}} \] = \[\sqrt {{{16} \over 5}} \]
\[ \therefore \] Length of chord of contact (AB) = \[{8 \over {\sqrt 5 }}\]
\[ \therefore \] AB2 = \[{{16 \times 16} \over {20}}\] = \[{{64} \over 5}\]