If from any point on the circle x^2+y^2+2 g x+2 f y+c=0 , tangents are drawn to the circle x^2+y^2+2 g x+2 f y+c ^2 + (g^2+f^2 ) ^2 =0, (0 < < 2 ) , then the angle between those tangents is

Step-by-step solution

Given equations of circles are c₁ x^2+y^2+2 g x+2 f y+c=0 Centre O(-g,-f) aligned & radius r₁= g^2+f^2-c & aligned c₂ x^2+y^2+ & 2 g x+2 f y & +c ^2 + (g^2+f^2 ) ^2 aligned aligned Centre O(-g,-f) radius r₂= g^2+f^2-c ^2 -g^2 ^2 -f^2 ^2 r₂= g^2 (1- ^2 )+f^2 (1- ^2 )-c ^2 = g^2+f^2-c as 0