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Math·Geometry and Trigonometry·Circles

hard

Circles $A$ and $B$ are graphed in the $xy$-plane. Circle $A$ is represented by the equation $(x-9{)}^2+(y+9{)}^2=81$ and intersects the $x$-axis at the point $(r,s)$. Circle $B$ has its center at $(r,s)$ and has a radius of the same length as circle $A$. Which equation represents circle $B$?

A

$x^2+(y-9{)}^2=81$

B

$x^2+(y+9{)}^2=81$

C

$(x-9{)}^2+y^2=81$

D

$(x+9{)}^2+y^2=81$