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The circle S(1) with centre C(1) ( a(1)...

The circle `S_(1) ` with centre `C_(1) ( a_(1), b_(1))` and radius `r_(1)` touches externally the circle`S_(2)` with centre `C_(2) ( a_(2), b_(2))` and radius `r_(2)`. If the tangent at their common point passes through the origin then `:`

A

`(a_(1)^(2)+a_(2)^(2))+(b_(1)^(2)+b_(2)^(2))=r_(1)^(2)+r_(2)^(2)`

B

`(a_(1)^(2)-a_(2)^(2))+(b_(1)^(2)-b_(2)^(2))=r_(1)^(2)-r_(2)^(2)`

C

`(a_(1)^(2)-b_(1)^(2))+(a_(2)^(2)+b_(2)^(2))=r_(1)^(2)+r_(2)^(2)`

D

`(a_(1)^(2)-b_(1)^(2))+(a_(2)^(2)+b_(2)^(2))=r_(1)^(2)+r_(2)^(2)`

Text Solution

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The correct Answer is:
B
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