Question

# Let $$C$$ be the circle with centre $$\left ( 0,0 \right )$$ and radius $$3$$ units. The equation of the locus of the mid points of chord of the circle $$C$$ that subtend an angle of $$\displaystyle \dfrac {2\pi }3$$ at its centre is

A
x2+y2=32
B
x2+y2=1
C
x2+y2=274
D
x2+y2=94

Solution

## The correct option is D $$x^{2}+y^{2}= \displaystyle \frac{9}{4}$$In $$\triangle CPB,$$$$\displaystyle \cos \frac{\pi}{3} =\frac{CP}{CB}=\frac{\sqrt{h^{2}+k^{2}}}{3}\Rightarrow h^{2}+k^{2}=\frac{9}{4}$$$$\displaystyle \therefore$$ Required locus is $$\displaystyle x^{2}+y^{2}=\frac{9}{4}$$Mathematics

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