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? \\(\bigcirc\\) \\(10\pi\\,\text{cm}^2\\) \\(\bigcirc\\) \\(16\pi\\,\text{cm}^2\\) \\(\bigcirc\\) \\(356\pi\\,\text{cm}^2\\) \\(\bigcirc\\) \\(676\pi\\,\text{cm}^2\\)

Explanation:

Step1: Calculate the length of \(GX\)

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

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 \(r = GX=26\mathrm{cm}\). Then \(A=\pi\times(26)^{2}\)

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Answer:

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