1. ## Inscribed Square

A square is inscribed in a small circle of a sphere whose great circle has a radius of 9cm. If the plane of the square is 6cm from the center of the sphere, find the perimeter of the square.

2. Hello, reiward!

Did you make a sketch?

A square is inscribed in a small circle of a sphere with radius 9 cm.
If the plane of the square is 6cm from the center of the sphere,
find the perimeter of the square.
Code:
* * *
*     |   x  *
A o - - - + - - - o B
*        |     *  *
6|   *
*         | *  9    *
*         o         *
*         C         *

*                 *
*               *
*           *
* * *

$AB$ is the side of the square.

Pythagorus says: . $x^2 + 6^2 \:=\:9^2 \quad\Rightarrow\quad x^2 \:=\:45 \quad\Rightarrow\quad x \:=\:3\sqrt{5}$

. . Then: . $AB \;=\;2x \;=\;6\sqrt{5}$

The perimeter is: . $4\left(6\sqrt{5}\right) \;=\;24\sqrt{5}\text{ cm}$