If the line \( p x+q y=1 \) touches the circle \( x^{2}+y^{2}=r^{2} \), prove that the point \( ...
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If the line \( p x+q y=1 \) touches the circle \( x^{2}+y^{2}=r^{2} \), prove that the point \( (p, q) \) lies on the circle \( x^{2}+y^{2}=r^{-2} \).
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