Question

A circle is centered at (0,0) and passes through (-3,0) and (3,0) in the standard (x,y) coordinate plane. A square is inscribed in the circle. What is the perimeter of the square?

A. 9
B. 12
C. 6√2
D.12√2
E. 18

Answer 1

D)

Explanation:

First we want to find the diameter of the circle, since we are only given coordinates we have to find the distance between these points this gives us the diameter.

| -3 + 3 | = 6 (|| = positive value)

The diameter is 6 now we can draw a inscribed square with each corner touching the circumference of the circle at 0,90,180,and 360 degrees.

To find the length of one side we have to use the radius of the circle with Pythagorean theorem.

3^2 + 3^2 = c^2 ; 18=c^2

sqrt = square root

Then square root both sides; sqrt(18) = sqrt(c^2)

sqrt(9) * sqrt(2) = sqrt(c^2) ; 3*sqrt(2) = c

This is one length to find the others we just multiply by four since the sides length of a square are all the same as each other. 4*(3*sqrt(2)) = Perimeter

12*sqrt(2)