A square is inscribed inside a circle. The square's vertices have coordinates R(0, 4), S(6, 2), T(4, -4), and U(-2, -2). Find the equation of the circle. (x-?)^2+y^2=?

Question

anonymous · Answer

guess we need the center and radius. let me draw a picture.  center will be halfway between the diagonal of the square, and radius will be half the length of the diagonal.
i am guessing that you can find both of those, but if not let me know

vishweshshrimali5 · Answer

satellite can u help me too please

anonymous · Answer

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anonymous · Answer

we can use $(0,4)$ and $(4,-4)$ as the two points 
we need the midpoint and the distance. let me know if  you need help finding those

anonymous · Answer

yes please

anonymous · Answer

to find the midpoint, take the average of the coordinates 
$$(\frac{0+4}{2},\frac{4-4}{2})$$
$$(2,0)$$ is the center

anonymous · Answer

now for the radius squared, find the square of the distance between $(2,0)$ and $(0,4)$ by pythagoras. it is 
$$2^2+4^2=4+16=20$$ now you have both the center $(2,0)$ and $r^2=20$ so you can write the equation