# Finding the center of a circle

Fun little inquiry project today – how do you find the center of a circle? We touched on this question in a project a few weeks ago, but it was nice to revisit it in a little more depth today.

We started with an introduction to the question and quick review of what we talked about last time. My younger son remembers that you can find the diameter of the circle by finding the longest chord in the circle with a ruler. My older son thinks about the idea of folding the circle in half to find the diameter. We’ll explore that second idea a little later in the project.

At the end of the last video my older son suggested that we could find the diameter of the circle by drawing a 90 degree angle on the circle. That seemed like an idea worth exploring more carefully.

After we find the diameter with the 90 degree angle the next question is how to find the center?

In the next part of the project I wanted to show a new way to find the center of the circle with a compass and straight edge. I had one way in mind, but my older son thought of a clever way by inscribing any triangle and finding the intersection of the perpendicular bisectors. This idea was fun to explore:

The last part of the project was playing around with the folding idea using our patty paper. This approach is actually a project in our Patty Paper Geometry book:

I had a hard time communicating the geometric idea going on with the patty paper – the idea is that two diameters intersect in the center of the circle. We talked around the idea for a while before getting to it.

So a fairly relaxed project. Lots of different ways to approach the problem – simple measuring, some basic construction ideas, and then a little folding. Hopefully a fun way to for kids to see that math problems can be approached from many different angles.