Question

you are given two circles. one circle has a radius of x and the other has a radius of y.

answer the following questions. leave all answers as fractions in simplest form in terms of x and y.

what is the scale factor of these circles?

• \\(\frac{x}{y}\\)
• \\(\frac{2x}{y}\\)

what is the ratio of the diameters of the first circle to the second circle?

• \\(\frac{x}{y}\\)
• \\(\frac{2x}{y}\\)

the ratio of the circumferences of these circles would be equal to the ratio of the radii.

these circles are congruent

Explanation:

Find the scale factor of the circles

$$ k = \frac{\text{Radius of first circle}}{\text{Radius of second circle}} = \frac{x}{y} $$

Find the ratio of the diameters

$$ \text{Ratio} = \frac{2x}{2y} = \frac{x}{y} $$

Determine the ratio of circumferences and geometric relationship

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Answer:

Question 1

What is the scale factor of these circles?

$$\frac{x}{y}$$

Question 2

What is the ratio of the diameters of the first circle to the second circle?

$$\frac{x}{y}$$

Question 3

The ratio of the circumferences of these circles would be equal to the ratio of the radii.

Question 4

These circles are similar.