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If the tangents at z(1), z(2) on the cir...

If the tangents at `z_(1)`, `z_(2)` on the circle `|z-z_(0)|=r` intersect at `z_(3)`, then `((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2)))` equals

A

`1`

B

`-1`

C

`i`

D

`-i`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)`
`(z_(3)-z_(1))/(z_(0)-z_(1))=((PA)/(AC))i` and `(z_(0)-z_(2))/(z_(3)-z_(2))=((BC)/(BP))i`
`:. ((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2)))=((PA)/(AC)xx(BC)/(PB))(-1)=-1`
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