The maximum area of the triangle formed by the complex coordinates `z, z_1,z_2` which satisfy the relations `|z-z_1|=|z-z_2|` and `|z-(z_1+z_2 )/2|<= r`,where `r>|z_1-z_2|` is

Options

A. `(1)/(2)|z_(1)-z_(2)|^(2)`
B. `(1)/(2) |z_(1)-z_(2)|r`
C. `(1)/(2)|z_(1)-z_(2)|^(2) r^(2)`
D. `(1)/(2)|z_(1)-z_(2)|^(2)`

Answer

B

Explanation

By the given conditions, the are of the triangle ABC is given by `(1//2)|z_(1)-z_(2)|r.`