Question

point g is the center of the small circle. point x is the center of the large circle. points g, y, and x are all on line segment gx. marco wants to create a new circle using \\( \overline { g x } \\) as a radius. what will be the area of marcos new circle? \\( 10 \pi \mathrm { cm } ^ { 2 } \\) \\( 16 \pi \mathrm { cm } ^ { 2 } \\) \\( 356 \pi \mathrm { cm } ^ { 2 } \\) \\( 676 \pi \mathrm { cm } ^ { 2 } \\)

Explanation:

Step1: Calculate the length of \(GX\)

Since \(GY = 10\) cm and \(YX=16\) cm, then \(GX=GY + YX\).
\(GX=10 + 16=26\) cm.

Step2: Use the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius. Here \(r = GX = 26\) cm.
Substitute \(r = 26\) into the formula: \(A=\pi\times(26)^{2}\).
\(A = 676\pi\) \(cm^{2}\).

Answer:

\(676\pi\) \(cm^{2}\) (the fourth option)