Question

Prove that the two circles shown below are similar. Circle X is shown with a center at negative 2, 8 and a radius of 6. Circle Y is shown with a center of 4, 2 and a radius of 3.

Answer 1

Answer:

They are similar for their radii, and perimeters have the  same ratio: 2

Step-by-step explanation:

The similarity of circles is proved, when we can compare the ratio, between the two radii and the two perimeter and it is the same.

2. The Circle X, has a radius of 6 and the circle Y has the radius of 3.

So let's do it:

$\frac{R_{x}}{R_{y}} =\frac{6}{3} =2$

3. Now let's check the Perimeters:

$\frac{2P_{x}}{2P_{y}}=\frac{2\pi*6}{2\pi*3}=2$

4. In addition to this, we can do this Geometrically, by inserting the Circle Y within the Circle X, and if dilate by the scale factor of 2 we'll have these two circumferences coincide.