(09.01 HC)
Prove that the two circles shown below are similar. (10 points)

Proved

Step-by-step explanation:

Given

Circle C

--- radius

--- center

Circle E

--- center

Required

Prove their similarity

Translate circle C 8 units up;

The rule is:

So, we have:

Translate circle C' 7 units right;

The rule is:

So, we have:

At this point, both circles now have the same center at (4,9)

The next step is to dilate circle E by 4/3

This will only affect radius and not the center of E

The rule is:

So, we have:

-- equal radii

--- equal center

Proved

47 - 90 = 43

43 - 180 = x

x = 137