Mathematics: 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

Square abcd is inscribed in circle p, with a diagonal

katier9407

31.12.2021

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

be the length of the apothem [line from center of square to midpoint of side]. Also, we let

be half the length of the side of the square.Since square,

and

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, is HALF of SIDE LENGTH, is:

$x=\frac{\sqrt{162}}{2}\\x=\frac{\sqrt{81}*\sqrt{2}}{2}\\x=\frac{9\sqrt{2}}{2}$

Since, and 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.

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billydeck30

17.01.2023

The probability of choosing of the blue tile and flip a coin are

1. P(BT) = 1/7 = 4

2. P(H or T) = 1/2 = 1.5

Step-by-step explanation:

1. P(BT) = 1/7

P(BT) = 1/7 + 2/7+ 3/7 + 4/7 + 5/7 + 6/7 + 7/7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28/7

P(BT) = 4

2. P(H or T) = 1/2 + 2/2 = 1 + 2/2 = 3/2 = 1.5

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