Through a fixed point \( (h, k) \) secants are drawn to the circle ...
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Through a fixed point \( (h, k) \) secants are drawn to the circle \( x^{2}+y^{2}=r^{2} \). Show that the locus of the mid-points of the secants intercepted by the circle is
P \( x^{2}+y^{2}=h x+k y \).
\( (1983,5 \mathrm{M}) \)
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