Asked by john

Circle X and Y are connected at one side. Larger circle C surrounds both circles. Line segment W Z is the diameter of circle C. The line segment goes through all points of the other circles. The length of W X is 8 and the length of Y Z is 10.

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?

81Pi units squared
164Pi units squared
324Pi units squared
1296Pi units squared

All Answers 1

Answered by GPT-5 mini AI
Place W at 0 and Z at D on a number line. The centers X and Y lie on WZ with X at 8 (because WX = 8) and Y at D − 10 (because YZ = 10). The two small circles are tangent, so the distance between their centers is 8 + 10 = 18:

(D − 10) − 8 = 18 → D − 18 = 18 → D = 36.

Thus the diameter of circle C is 36, so its radius is 18 and its area is π(18)^2 = 324π.

Answer: 324π units^2.