InterMath | Workshop Support | Write Up Template

Title
Intersecting Circles

Problem Statement
Construct two intersecting circles that pass through each other’s center. What is/are the relationship(s) between the two circles? Construct a segment between the centers and the intersection of the circles? Describe the significance of these two segments.

Problem setup
What is/are the relationship(s) between circles that pass through each other’s center? Also describe what you notice about the segments between the centers and the intersections of the circles. This problem is similar to the ones we do in class in that through manipulations we discover the properties as well as relationships between the properties of different shapes. It is also similar to the problems we worked about circles involving diameter, circumference and area.

Plans to Solve/Investigate the Problem
First, I plan to try to visualize two circles each passing through each other’s center and what it would look like. Next, I will construct the two circles and the segments between the centers and the intersections using Geometer’s sketchpad. Once I have the figures constructed I will manipulate them to see what I notice. Finally, I will make conjectures about the relationships between the two circles as well as the two segments based on the construction and my manipulations.

Investigation/Exploration of the Problem
I will begin by trying to visualize two circles intersecting each others’ centers. Afterward I will construct the two circles and the two lines and perform the calculations on Sketchpad. Once I have the figure constructed I will drag on it so that it increases and decreases as I pay attention to how the properties are changing. After reviewing my calculations I determined that the two circles were congruent. They had congruent radii, and circumference. Their areas were also congruent. I also determined that the two lines were perpendicular to each other and that the segment connecting their midpoints was the radius for both circles.

Extensions of the Problem
Would it be possible for there to be three circles intersecting each others midpoint? What about four? How are they different?

Author & Contact
Nathan Little
nlittle@aug.edu

Link(s) to resources, references, lesson plans, and/or other materials
My constructions
Intermath

U Important Note: You should compose your write-up targeting an audience in mind rather than just the instructor for the course. You are creating a page to publish it on the web.