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{gx}) as a radius. what will be the area of marcos new circle? (16pi cm^{2}) (356pi cm^{2}) (676pi cm^{2}) (10pi cm^{2})

Explanation:

Step1: Calculate the length of \( GX \)

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

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 \( r = GX = 26\mathrm{cm} \).
Substitute \( r = 26 \) into the formula: \( A=\pi\times(26)^{2}\)
\( A = 676\pi\mathrm{cm}^{2}\)

Answer:

\(676\pi\mathrm{cm}^{2}\)