The chord of contact of tangents drawn from a point on the circle `x^2 + y^2 = a^2` to the circle `x^2 + y^2 = b^2` touches the circle `x^2 + y^2=c^2` Show that a, b, c are in G.P.
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Let (h,k) be the point `x^(2)+y^(2)=a^(2)`. Then, `h^(2)k^(2)=a^(2)` (1) The equation of the chord of contact of tangents drawn from (h,k) to `x^(2)+y^(2)=b^(2)` is `hx+ky=b^(2)` (2) This touches the circle `x^(2)+y^(2)=c^(2)`. Therefore, `|(-b^(2))/(sqrt(h^(2)+k^(2)))|` or `|(-b^(2))/(sqrt(a^(2)))|` [Using (1)] or `b^(2)=ac` Therefore, a,b, and c are in GP.
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