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 GX as a radius. What will be the area of Marco’s new circle?

A. 10 pie cm2
B. 16 pie cm2
C. 356 pie cm2
D. 676 pie cm2

Answer 1

The answer 
if Marco wants to create a new circle using GX as a radius,
so GX = r = 10 cm + 16 cm = 26 cm
the area of a circle is 

A = pie x r², so the new circle's area should be A = pie x 26² = 676 pie cm²
the true answer is 

D. 676 pie cm2

Answer 2

Answer-

The area of Marco’s new circle will be $676\pi$ cm²

Solution-

Point G is the center of the small circle.

Point X is the center of the large circle.

Points G, Y, and X are colinear.

Hence,

GY = 10 cm

YX = 16 cm

So, GX = GY + YX = 10 + 16 = 26 cm

Hence, area of the circle with radius as GX will be,

$\text{Area of circle}=\pi \times \text{Radius}^2\\\\=\pi \times GX^2\\\\=\pi \times 26^2\\\\=676\pi\ cm^2$

Therefore, the area of Marco’s new circle will be $676\pi$ cm²