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Question

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


Solution

For general circle $$x^2+y^2+2gh+2fy+c=0$$ , 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 $$90^{0}$$

Mathematics

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