Question

george is given two circles, circle o and circle x, as shown. if he wants to prove that the two circles are similar, what would be the correct second step in his proof? given: the radius of circle o is r, and the radius of circle x is r. prove: circle o is similar to circle x. 1. c = 2πr and c = 2πr by the definition of circumference. 2. ____________ 3. d = 2r and d = 2r by the definition of diameter. 4. $\frac{d = 2r}{d = 2r}$ and $\frac{d}{d}=\frac{r}{r}$ by the division property of equality. 5. $\frac{d = 2r}{d = 2r}$ and $\frac{r}{r}=\frac{r}{r}$ by the substitution property. 6. circle o is similar to circle x because all the linear dimensions are in the same proportion.

Explanation:

Step1: Recall similarity property

All circles are similar if the ratio of their corresponding linear - dimensions (radius, diameter, circumference) is constant. After finding the circumferences in step 1, we can find the ratio of the circumferences.

Step2: Calculate ratio of circumferences

The ratio of the circumference of circle \(O\) to the circumference of circle \(X\) is \(\frac{C}{C'}=\frac{2\pi r}{2\pi r'}\)

Answer:

\(\frac{C}{C'}=\frac{2\pi r}{2\pi r'}\)