Question

ming transformations on circles concentric circles with center g have radii 5 and 11 as shown. which would prove that the circles are similar? dilate the smaller circle by a factor of if the circles were not concentric, what additional step would be needed to prove they are similar? one of the circles so that the circles have the same center

Explanation:

Step1: Recall similarity of circles

Two circles are similar if one can be obtained from the other by dilation. The ratio of the radii of the two circles gives the dilation factor.

Step2: Calculate dilation factor

The radius of the larger circle is $r_1 = 11$ and the radius of the smaller circle is $r_2=5$. The dilation factor $k$ from the smaller - circle to the larger circle is $k=\frac{r_1}{r_2}=\frac{11}{5}$.

Step3: Consider non - concentric circles

If the circles are not concentric, in addition to dilation, a translation is needed to move one of the circles so that their centers coincide.

Answer:

Dilate the smaller circle by a factor of $\frac{11}{5}$; Translate one of the circles so that the circles have the same center.