For this problem, (a,b) is a point in the x-y coordinate plane and r is a positive number.
Using a translation and a dilation, show how to transform the circle with radius r centered at (a,b) into the circle of radius 1 centered at (0,0) . Explain how to use your work in part (a) to show that any two circles are similar.
A set of exercises, commentary, and solutions from Illustrative Mathematics
Teacher and Student versions of full lesson from engageNY, Circle similarity is last topic.
Define the angle measure of arcs, and understand that arcs of equal angle measure are similar. Restate and understand the inscribed angle theorem in terms of arcs: The measure of an inscribed angle is half the angle measure of its intercepted arc. Explain and understand that all circles are similar.
Sean has two circles, one with a radius of 1 inch and another with a radius of 3 inches.
What is the ratio between the radii of the circles? What is the scale factor between the two circles? What is the ratio between the circumferences of the circles? What is the ratio between the areas of the circles? What do area ratios and circumference ratios have to do with scale factor?
Lessons, videos, exercises, and text from CK-12. Additional resources available at this site.