Question

George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct first step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.

Answer 1

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:

`r'{\cdot}x=r`⇒
`x=(r)/(r')`

A translation followed by a dilation with scale factor
`(r)/(r')` will map one circle to the other, thus proving the given both circles similar.

Therefore, circle O is similar to circle X.

Answer 2

Answer: definition of circumference

c= 2pir and c = 2 Pi r by the definition of circumference

Step-by-tep explanation: