A line meets the coordinate axes at `A` and `B` . A circle is circumscribed about the triangle `O A Bdot` If `d_1a n dd_2` are distances of the tangents to the circle at the origin `O` from the points `Aa n dB` , respectively, then the diameter of the circle is (a)`(2d_1+d_2)/2` (b) `(d_1+2d_2)/2` (c)`d_1+d_2` (d) `(d_1d_2)/(d_1+d_2)`

Options

A. `(2d_(1)+d_(2))/(2)`
B. `(d_(1)+2d_(2))/(2)`
C. `d_(1)+d_(2)`
D. `(d_(1)d_(2))/(d_(1)+d_(2))`

Answer

3

Explanation

Let the circle be `x^(2)+y^(2)+2gx+2fy=0`.

Tangent at the origin is
`gx+fy=0`
`d_(1)=(2g^(2))/(sqrt(g^(2)+f^(2)))` and `d_(2)=(2f^(2))/(sqrt(g^(2)+f^(2)))`
or `d_(1)+d_(2) = 2sqrt(g^(2)+f^(2))`
`=` Diameter of the circle