The locus of the mid-points of the chords of the circle of radius r which subtend an angle at any point on the circumference of the circle is a concentric circle with radius equal to
Let the equation of the circle be . The chord which subtends an angle at the circumference will subtend a right angle at the centre.
So, chord joining A(r, 0) and B(0, r) subtends a right angle at the centre (0,0). Mid point of AB is
, which is radius of locus of C.
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