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Square ABCD is inscribed in circle P, with a diagonal that is 18 centimeters long. Find the exact length of the apothem of square ABCD.
a. 18√2
b. 9√2
c. 9√2 over 2
d. 9 over 2

Respuesta :

Benjamin16
[tex]d=a \sqrt{2} \\ \\ a \sqrt{2} =18 \\ \\ a= \frac{18}{ \sqrt{2} } = \frac{18 \sqrt{2} }{2}=9 \sqrt{2} \\ \\ x= \frac{a}{2} \\ \\ x= \frac{9 \sqrt{2} }{2} [/tex]
TaeKwonDoIsDead

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 [tex]y[/tex] be the length of the apothem [line from center of square to midpoint of side].
  • Also, we let [tex]x[/tex] be half the length of the side of the square.
  • Since square, [tex]x[/tex] and [tex]y[/tex] are equal

Let's find the side length of the square using pythagorean theorem:

[tex](Side Length)^{2}+(Side Length)^{2}=18^{2}\\2SideLength^{2}=324\\SideLength^{2}=162\\SideLength=\sqrt{162}[/tex]

Since, [tex]x[/tex] is HALF of SIDE LENGTH, [tex]x[/tex] is:

[tex]x=\frac{\sqrt{162}}{2}\\x=\frac{\sqrt{81}*\sqrt{2}}{2}\\x=\frac{9\sqrt{2}}{2}[/tex]

Since, [tex]x[/tex] and [tex]y[/tex] are equal, we can say [tex]y=\frac{9\sqrt{2}}{2}[/tex]

Apothem's length is [tex]\frac{9\sqrt{2}}{2}[/tex]. Answer choice C is right.


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