Question

Given these two circles, which of the following statements is true?

A. Circle X is never similar to circle Y.
B. Circle X is always similar to circle Y.
C. Circle X is similar to circle Y if the length of each radius is a whole number.
D. Circle X is sometimes similar to circle Y.

The answer is NOT D.

Answer 1

Option B: Circle X is always similar to circle Y.

Explanation:

A circle is a set of points which is equidistant from the center of the circle.

Let the radius of the circle X be $r_1$

Let the radius of the circle Y be $r_2$

Now, we shall prove that the Circle X is always similar to Circle Y.

From the figure, we can see that the circle Y is increased when comparing it with circle X.

Thus, the scale factor x is needed to increase circle X.

Hence, we have,

$r_{1}\times x=r_{2}$

      $x=\frac{r_{2}}{r_{1}}$

Thus, the two circles is always similar.

Hence, Circle X is always similar to circle Y.

Therefore, Option B is the correct answer.