Answer:
C
Step-by-step explanation:
The Square ABCD inscribed in a circle is shown in the picture attached.
- The diagonal is broken down into two 9 cm parts as shown.
- We let \(y\) be the length of the apothem [line from center of square to midpoint of side].
- Also, we let \(x\) be half the length of the side of the square.
- Since square, \(x\) and \(y\) are equal
Let's find the side length of the square using pythagorean theorem:
\((Side Length)^{2}+(Side Length)^{2}=18^{2}\\2SideLength^{2}=324\\SideLength^{2}=162\\SideLength=\sqrt{162}\)
Since, \(x\) is HALF of SIDE LENGTH, \(x\) is:
\(x=\frac{\sqrt{162}}{2}\\x=\frac{\sqrt{81}*\sqrt{2}}{2}\\x=\frac{9\sqrt{2}}{2}\)
Since, \(x\) and \(y\) are equal, we can say \(y=\frac{9\sqrt{2}}{2}\)
Apothem's length is \(\frac{9\sqrt{2}}{2}\). Answer choice C is right.
