Question

Please help!! Question is attached!

Answer 1

D) 72

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:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the center (2, 5) and the point on the circle (5, 2). Substitute:

`r=√((5-2)^2+(2-5)^2)=√(3^2+(-3)^2)=√(9+9)=√(9\cdot2)=\sqrt9\cdot\sqrt2=3\sqrt2`

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

`a=2r\to a=2(3\sqrt2)=6\sqrt2`

The formula of an area of a square:

`A=a^2`

Substitute:

`A=(6\sqrt2)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\A=6^2(\sqrt2)^2\qquad\text{use}\ (√(a))^2=a\\\\A=(36)(2)=72`