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Licemer1 [7]
3 years ago
5

Please help!! Question is attached!

Mathematics
1 answer:
balu736 [363]3 years ago
8 0

Answer:

<h2>D) 72</h2>

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:

d=\sqrt{(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=\sqrt{(5-2)^2+(2-5)^2}=\sqrt{3^2+(-3)^2}=\sqrt{9+9}=\sqrt{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}\ (\sqrt{a})^2=a\\\\A=(36)(2)=72

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