Question

1. circle o is similar to circle x because all the linear dimensions are in the same proportion.

a. c = πr and c = πr by the definition of area of a circle.
b. c = πr² and c = π(r)² by the definition of area of a circle.
c. c = 2r and c = 2r by the definition of circumference.
d. c = 2πr and c = 2πr by the definition of circumference.

Explanation:

Step1: Recall circle - related formulas

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle. For circle $O$ with radius $r$ and circle $X$ with radius $r'$, their circumferences are $C = 2\pi r$ and $C'=2\pi r'$ respectively according to the circumference formula.

Step2: Analyze options

Option A and B use the wrong formulas for circumference (they use area - related forms). Option C uses the diameter formula ($d = 2r$) instead of the circumference formula. Option D is correct as it applies the correct circumference formula for both circles.

Answer:

D. $C = 2\pi r$ and $C'=2\pi r'$ by the definition of circumference.