Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of ${{2\pi } \over 3}$ at its center is :
${x^2} + {y^2} = {3 \over 2}$
${x^2} + {y^2} = 1$
${x^2} + {y^2} = {{27} \over 4}$
${x^2} + {y^2} = {{9} \over 4}$
Solution
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