Question

point g is the center of the small circle. point x is the center of the large circle. points g, h, and x are on line segment gx. what would be the area of a new circle that has line segment gx as its diameter? diagram: small circle with center g, large circle with center x; segment gh = 6 cm, segment hx = 8 cm options: 16π cm², 36π cm², 49π cm², 98π cm²

Explanation:

Step1: Find the length of GX

From the diagram, \( GH = 6\space cm \) and \( HX = 8\space cm \). So, \( GX=GH + HX=6 + 8 = 14\space cm \).

Step2: Find the radius of the new circle

The diameter of the new circle is \( GX = 14\space cm \), so the radius \( r=\frac{GX}{2}=\frac{14}{2}=7\space cm \).

Step3: Calculate the area of the new circle

The formula for the area of a circle is \( A=\pi r^{2} \). Substituting \( r = 7\space cm \), we get \( A=\pi\times7^{2}=49\pi\space cm^{2} \).

Answer:

\( 49\pi\space cm^{2} \) (corresponding to the option \( 49\pi\space cm^{2} \))