Answer:
D) 72
Step-by-step explanation:
A distance between a center of a circle and other point on the circle is equal to a length of a radius.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the center (2, 5) and the point on the circle (5, 2). Substitute:
[tex]r=\sqrt{(5-2)^2+(2-5)^2}=\sqrt{3^2+(-3)^2}=\sqrt{9+9}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=3\sqrt2[/tex]
The length of the side of the square is equal to twice the length of the radius of the circle inscribed in the square.
Therefore:
a - length of the side of the square
[tex]a=2r\to a=2(3\sqrt2)=6\sqrt2[/tex]
The formula of an area of a square:
[tex]A=a^2[/tex]
Substitute:
[tex]A=(6\sqrt2)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\A=6^2(\sqrt2)^2\qquad\text{use}\ (\sqrt{a})^2=a\\\\A=(36)(2)=72[/tex]
