The triangle formed by `A(z_(1)), B(z_(2)) and C(z_(3))` has its circumcentre at origin .If the perpendicular form A to BC intersect the circumference at `z_(4)` then the value of `z_(1)z_(4) + z_(2)z_(3)` is

Explanation

`arg((z_(4)-z_(1))/(z_(3)-z_(2)))=(pi)/(2)`
`implies" "(z_(4)-z_(1))/(z_(3)-z_(2))+(bar(z)_(4)-bar(z)_(1))/(bar(z)_(3)-bar(z)_(2))=0`
`implies" "(z_(4)-z_(1))/(z_(3)-z_(2))+((r^(2))/(z_(4))-(r^(2))/(z_(1)))/((r^(2))/(z_(3))-(r^(2))/(z_(2)))=0,`
Where r is radius.
`implies" "(z_(4)-z_(1))/(z_(3)-z_(2))+(z_(2)z_(3))/(z_(1)z_(4))((z_(4)-z_(1))/(z_(3)-z_(2)))=0`
`impliesz_(1)z_(4)+z_(2)z_(3)=0`