Answer:
Step-by-step explanation:
Given: The radius of circle O is r, and the radius of circle X is r'.
To prove: Circle O is similar to circle X.
Proof: Move the center of the smaller circle onto the center of the largest circle. Translate the circle X by the vector XA onto circle O. The circles now have the same center.
A dilation is needed to increase the size of circle X to coincide with the circle O. A value which when multiplied by r' will create r.
The scale factor x to increase X:
[tex]r'{\cdot}x=r[/tex]⇒[tex]x=\frac{r}{r'}[/tex]
A translation followed by a dilation with scale factor [tex]\frac{r}{r'}[/tex] will map one circle to the other, thus proving the given both circles similar.
Therefore, circle O is similar to circle X.
