If from any point `P` on the circle `x^2+y^2+2gx+2fy+c=0`, tangents are drawn to the circle `x^2+y^2+2gx+2fy+csin^2 alpha+(g^2+f^2)cos^2 alpha=0`, then the angle between the tangents is :
(A) `alpha`
(B) `2 alpha`
(C) `alpha/2`
(D) `alpha/3`

Explanation

P(h,k) to the cords

`x^2+y^2+2xy+2fy=0`

`T=h^2+k^2+2gh+2fk+c`

`T=h^2+k^2+2gh+2fk+sin^alpha+(g^2+f^2)cos^2alpha`

`sintheta(h,k)` lies on the circle `x^2+y^2+2gx+2fy+c=0`

`t^2=(h^2+k^2gh+2fk+c)+csin^alpha+(g^2+f^2)cos^2alpha-c`

`=(g^2+f^2)cos^2alpha-c(1-sin^2alpha)`

`r^2=g^2f^2-(csin^2alpha+(g^2+f^2)cos^2alpha)`

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