The locus of the middle points of the chords of the circle of radiu...

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The locus of the middle points of the chords of the circle of radius \( r \) which subtend an angle \( \pi / 4 \) at any point on the circumference of the circle is a concentric circle with radius equal to
(a) \( r / 2 \)
(b) \( 2 r / 3 \)
(c) \( r / \sqrt{2} \)
(d) \( r / \sqrt{3} \)
(W)
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