If two tangents are drawn from a point on the circle $x^{2} + y^{2} = 50$ to the circle $x^{2} + y^{2} = 25$ , then find the angle between the tangents

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Solution

For general circle $x^{2} + y^{2} + 2 g h + 2 f y + c = 0$ , Equation of director circle = $(x + g)^{2} + (y + f)^{2} = 2 (g^{2} + f^{2} - c)$
(Director Circle - Locus of a point from where tangents to a given circle are perpendicular )
So $x^{2} + y^{2} = 50$ act as the director circle for the circle $x^{2} + y^{2} = 25$
Thus by definition of director circle angle between tangents will be $90^{0}$

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Similar questions

x^{2} + y^{2} = 25

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1,

x^{2} + y^{2} = 50

x^{2} + y^{2} = 25

x^{2} + y^{2} = 41

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

x^{2} + y^{2} = a^{2}

x^{2} + y^{2} = b^{2}

(a > b)

k {sin}^{- 1} \frac{b}{a}

k =

x^{2} + y^{2} = 41

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

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