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Asked by Vishnusasidharan | 05 Apr, 2010, 08:12: PM Expert Answer

The chord will be hypotenuse of the right angled triangle with remaining two sides being the radius of the circle, which is 2.

The length of hypotenuse = (22+22) = 2 2

The length of 1/2 hypotenuse = 2

The length of perpendicular bisector, (22-2) = 2

Let the coordinates of the midpoint of the chord be (x,y).

The distance from origin, (x2+y2) = length of perpendicular bisector = 2

Squaring both sides,

x2+y2 = 2,

Hence the locus is a circle with radius 2.

Regards,

Team,

TopperLearning

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