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The circle S1 with centre C1 (a1, b1) an...

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_(2)^(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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