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?
○ $16\pi \text{ cm}^2$
○ $36\pi \text{ cm}^2$
○ $49\pi \text{ cm}^2$
○ $98\pi \text{ cm}^2$
(length of gh is 6 cm, length of xh is 8 cm)

Explanation:

Step1: Find length of GX

$GX = 6\ \text{cm} + 8\ \text{cm} = 14\ \text{cm}$

Step2: Find radius of new circle

$\text{Radius} = \frac{GX}{2} = \frac{14}{2} = 7\ \text{cm}$

Step3: Calculate area of new circle

$\text{Area} = \pi r^2 = \pi \times 7^2$

Answer:

$49\pi\ \text{cm}^2$ (Option C)