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

Options

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)`

Answer

B