Chapter 11
Circle Geometry
A circular window can look simple until you add a few straight bars. How much freedom do those bars have, and which parts of the design depend on the circular frame? A sketch can suggest answers, but its appearance cannot settle them. Circle geometry gives us a way to ask precise questions about straight lines and angles in a round figure. What can the shape itself tell us when some measurements are hidden?
What You'll Explore
6 lessons.
Progress can't be saved in this browser, so lesson statuses can't be set here.
-
Two straight bars across a round window can sit in very different places. What might their positions tell us about the parts of the circle they meet? Explore relationships between chords and arcs, with the center providing another point of view.
-
Imagine a straight path beside a circular pond. What changes as the path shifts toward the pond? Examine tangents and secants, and the questions that arise when lines meet one circle or when two circles sit close together.
-
Suppose two markers stay fixed on the edge of a circular stage while your viewpoint moves around it. What happens to the angle between your lines of sight? Explore that question through inscribed angles and the arcs they face.
-
Four points around a circle can become the corners of a quadrilateral, but what does sharing that circle mean for its angles? Look into the questions raised by cyclic quadrilaterals, including whether an angle clue can help decide when four corners belong on one circle.
-
Beyond angles with vertices on the circle, what questions appear when two lines meet inside it or outside it? Compare these arrangements and investigate how the meeting point affects which arcs are relevant to an angle.
-
Lengths bring a new puzzle when lines through one point cut across a circle or touch its edge. How might the resulting segments be connected? Explore segment products and power of a point, with careful attention to which lengths a diagram is describing.