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A(z(1)),B(z(2)),C(z(3)) are the vertices...

`A(z_(1)),B(z_(2)),C(z_(3))` are the vertices of a triangle ABC inscrible in the circle `|z|=2` . Internal angle bisector of the angle A meets the circumcircle again at `D(z_(4))`.

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(2)`

D

`(2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly ,OD bisects `/_BOC ` of isosceles triangle BOC.
Thus angle between segments OD andBC is `pi//2`
`therefore arg((z_(4))/(z_(2) -z_(3))) = (pi)/(2)`
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