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Locus of the midpoints of radii or equal chords of a circle: a concentric circle

This type of question, asked 2 times: CDS 2 2016, CDS 1 2018. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    70
    ABCDAABCDA is a con-cyclic quadrilateral of a circle ABCDABCD with radius rr and centre at OO. If ABAB is the diameter and CDCD is parallel and half of ABAB and if the circle completes one rotation about the centre OO, then the locus of the middle point of CDCD is a circle of radius

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  2. Question 2

    CDS 1 2018

    76
    The locus of the mid-points of the radii of length 16 cm of a circle is

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