30. Olympic Flag You are using a math software program to design a pattern for an Olympic flag. In addition
to the dimensions shown in the diagram, the distance between any two adjacent rings in the same row is 3
inches.

a. Use the given dimensions to write equations representing the outer circles of the five rings. Use
inches as units in a coordinate plane with the lower left corner of the flag at the origin.

b. Each ring is 3 inches thick. Explain how you can adjust the equations of the outer circles to write
equations representing the inner circles.

Step-by-step explanation:

The general equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center of the circle and r is the radius.

The radius of each outer circle is 13".  The equations are:

(x − 28)² + (y − 44)² = 13²

(x − 57)² + (y − 44)² = 13²

(x − 86)² + (y − 44)² = 13²

(x − 42.5)² + (y − 31)² = 13²

(x − 71.5)² + (y − 31)² = 13²

Graph: desmos.com/calculator/4j6dpgd9wz

The radius of each inner circle is 3" less than the outer circle, or 10".  We can adjust the equations to represent the inner circles by replacing the 13 with a 10.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)