Question

Prove that the two circles shown below are similar.

Answer 1

Answer:

Proved

Step-by-step explanation:

Given

Circle B

$(x,y) = (-1,5)$ --- center

$r = 4$ ---radius

Circle D

$(x,y) = (7,4)$ --- center

$r = 2$ ---radius

Required

Prove the similarity

First, we shift circle B, 8 units right.

The rule is:

$(x,y) \to (x+8,y)$

So, we have:

$(-1,5) \to (-1+8,5)$

$(-1,5) \to (7,5)$

Next, we shift the resulting image of B, 1 unit down.

The rule is:

$(x,y) \to (x,y-1)$

So, we have:

$(7,5) \to (7,5-1)$

$(7,5) \to (7,4)$

At this point, both circles have the same center

$(x,y) = (7,4)$

Compress the image of B by a dilation of 1/2.

This only affects the radius.

i.e.

$r =r_B * 1/2$

$r =4 * 1/2$

$r =2$

Now, the have the same center and the same radii.

Proved