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If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+3)...

If `|z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+3)` , then prove that `z_1, z_2, z_3` are vertices of a right angled triangle.

Text Solution

Verified by Experts

For circe, `|z|=2`, points z = 2 and z=- 2 are end points of diameter.
`rArr arg ((z-2)/(z+2)) = pm(pi)/(2)`
`rArr arg ((z_(1)-z_(3))/(z_(2)-z_(3))) = (pi)/(2)`
Therefore, `z_(1),z_(2)` and `z_(3)` are the vertices of a right angled triangle.
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