Question

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: Calculate the dilation factor

The formula for the dilation factor \(k\) when dilating a circle with radius \(r_1\) to a circle with radius \(r_2\) is \(k=\frac{r_2}{r_1}\). Here, \(r_1 = 5\) (radius of the smaller circle) and \(r_2=11\) (radius of the larger circle). So, \(k=\frac{11}{5}\).

Step2: Determine the transformation for non - concentric circles

If two circles are not concentric, we need to use a translation. A translation is a transformation that moves every point of a figure or space by the same distance in a given direction. We can translate (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.