Question

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

Answer 1

Answer:

Proved

Step-by-step explanation:

Given

Circle C

$R = 4$ --- radius

$(x,y) = (-3,1)$ --- center

Circle E

$r= 3$

$(x,y) = (4,9)$ --- center

Required

Prove their similarity

Translate circle C 8 units up;

The rule is:

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

So, we have:

$(-3,1) \to (-3,1+8)$

$(-3,1) \to (-3,9)$

Translate circle C' 7 units right;

The rule is:

$(x,y) \to (x+7,y)$

So, we have:

$(x,y) \to (-3+7,9)$

$(x,y) \to (4,9)$

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:

$r' = r * \frac{4}{3}$

$r' = 3 * \frac{4}{3}$

$r' = 4$

So, we have:

$R = r' = 4$ -- equal radii

$(x,y) \to (4,9)$ --- equal center

Proved