Question

Why is circle 1 similar to circle 2?

Answer 1

Answer:  The answer is given below.

Step-by-step explanation: The given circles are:

Circle 1: centre (2, 3) and radius 4  

Circle 2: centre (2, 3) and radius 12.

The equations of circle 1 and circle 2 are respectively given as :

$(x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.$

These two circles are drawn on the graph as shown in the attached figure.

We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor

$S=\dfrac{12}{4}=3.$

Thus, the two circles are similar.

Answer 2

The correct answer is

Circle 2 is a dilation of circle 1 with a scale factor of 3.