Question

line segment wx is the radius of circle x, and line segment zy is the radius of circle y. points w, x, c, y, and z are all on line segment wz.
what is the area of circle c, which passes though points w and z?
○ $81\pi$ units$^{2}$
○ $164\pi$ units$^{2}$
○ $324\pi$ units$^{2}$
○ $1296\pi$ units$^{2}$

Explanation:

Step1: Find length of WZ

WX is radius 8, so WX = 8, and since X is center of its circle, WX = XC = 8. ZY is radius 10, so ZY = 10, and Y is center of its circle, so YZ = CY = 10.
$WZ = WX + XC + CY + YZ = 8 + 8 + 10 + 10 = 36$

Step2: Find radius of circle C

Circle C passes through W and Z, so WZ is its diameter. Radius $r = \frac{WZ}{2}$
$r = \frac{36}{2} = 18$

Step3: Calculate area of circle C

Area formula: $A = \pi r^2$
$A = \pi \times 18^2 = 324\pi$

Answer:

$324\pi$ units²