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A(z1),B(z2) and C(z3) are the vertices o...

`A(z_1)`,`B(z_2)` and `C(z_3)` are the vertices of triangle ABC inscribed in the circle |z|=2,internal angle bisector of angle A meets the circumcircle again at `D(z_4)`.Point D is:

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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