5. Given the circle $x^{2}+y^{2}=1$, point $A(1,0)$, and $\triangle A B C$ inscribed in the circle, with $\angle B A C=60^{\circ}$. When $B C$ moves on the circle, the equation of the trajectory of the midpoint of $B C$ is
A. $x^{2}+y^{2}=\frac{1}{2}$
B. $x^{2}+y^{2}=\frac{1}{4}$
C. $x^{2}+y^{2}=\frac{1}{2}\left(x<\frac{1}{2}\right)$
D. $x^{2}+y^{2}=\frac{1}{4}\left(x<\frac{1}{4}\right)$
5. D Hint: Use geometric method.



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5. D Hint: Use geometric method.