Question

Why is circle 1 similar to circle 2?

Answer 1

We have a golden rule about similarity of figures. It is "All circle are always similar to each other".

In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.

The ratio of radii of two circles is called the scale factor of dilation between them.

Given are two circles with following information :-

Circle 1: center (0, 9) and radius 14

Circle 2: center (0, 9) and radius 7

Finding the ratio of their radii :-

$\frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2$

So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.

Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.

Answer 2

A) Circle 1 is a dilation of circle 2 with a scale factor of 2.
1/2 = r1/r2 = 14/7 = 2 --> dilation scale factor