If `z_(1), z_(2), z_(3), z_(4)` are complex numbers in an Argand plane satisfying `z_(1)+z_(3)=z_(2)+z_(4)`. A compex number `'z'` lies on the line joining `z_(1)` and `z_(4)` such that `Arg((z-z_(2))/(z_(1)-z_(2)))=Arg((z_(3)-z_(2))/(z-z_(2)))`. It is given that `|z-z_(4)|=5,|z-z_(2)|=|z-z_(3)|=6` then

Options

A. area of triangle formed by `z,z_(1),z_(2)` is `3sqrt(7)` sq units
B. area of the triangle formed by `z, z_(3), z_(4)` is `(15sqrt(7))/3` sq. units
C. area of the quadrilateral formed by the points `z_(1),z_(2),z_(3),z_(4)` taken in orders is `(27sqrt(7))` sq. units
D. area of the quadrilateral formed by the points `z_(1),z_(2),z_(3),z_(4)` taken in order is `(27sqrt(7))/4` sq. units

Answer

A, B, C

Explanation

`a=b+5`
and `b/6=6/a`
`implies ab=36`
`b^(2)+5b-36=0`
`implies b=4`