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Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.

What is the area of circle C, which passes though points W and Z?

81
164
324
1296

Line segment WX is the radius of circle X and line segment ZY is the radius of circle Y Points W X C Y and Z are all on line segment WZ What is the area of circ class=

Respuesta :

merlynthewhizz
Point D is the midpoint of the outer circle that we aim to find the area of

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be [tex]x[/tex] and CY be [tex]10-x[/tex]

The radius of the outer circle can be written as [tex]8+8+x[/tex] or [tex]10+10-x[/tex] which we can equate to find the value of [tex]x[/tex]

[tex]8+8+x=10+10-x[/tex]
[tex]16+x=20-x[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]

Therefore, the radius of the circle is [tex]8+8+2=18[/tex]

And hence the area of the circle is [tex] \pi (18^{2})[/tex]=324[tex] \pi [/tex]
Ver imagen merlynthewhizz

To solve the problem we will first find the radius of the circle and then find the area of the circle c.

The correct option is c which is 324π.

Explanation

Given to us:

  • Radius of circle X = WX = 8 units,
  • Radius of circle Y = ZY = 10 units,

What is Diameter of Circle C?

As, it is mentioned in the question that the points W, X, C, Y, and Z are all on line segment WZ.Therefore, we can write it as,

Diameter of Circle C = Diameter of Circle X + Diameter of Circle Y,

Diameter of circle X, [tex]D_X[/tex] = 2 x WX = 2 x 8 = 16 units;

Diameter of circle Y, [tex]D_Y[/tex] = 2 x Zy = 2 x 10 = 20 units;

So, Diameter of Circle C = Diameter of Circle X + Diameter of Circle Y Diameter of Circle C = [tex]D_X + D_Y =16+20=36\ units[/tex]

Area of Circle C

we know area of a circle [tex]=\pi (radius)^2=\frac{\pi}{4} (diameter)^2[/tex],

Therefore,

[tex]\begin{aligned}Area\ of\ the\ circle\ C&= \frac{\pi}{4} (diameter)^2\\&= \frac{\pi}{4} (36)^2\\&=324\pi\ units\end{aligned}[/tex].

Hence, the the area of circle C is 324π.

Learn more about Area of the circle:

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