Lab 2: Orthogonal Circles and Inversion

Much of this lab will use sections of Chapter 9 of GTC. Also, notice that the term "pencil of circles" is used and partly explained in GTC. Pencils are special sets of circles that will be explained more fully in class later.

OPTIONS: There is a Sketchpad Sketch that you can download that will lead you through the lab. This is probably the best course. However it will be very valuable for you to also read this page after working on the sketch and also to read the sections of GTC.

Link to lab02.gsp

Section 1. Inversion of a Point and Orthogonal Circles

Part A. Construction of circle orthogonal to circle c at a given point and through a point A not on c.

Part B. Tracing orthogonal circles

Part C. A first construction for inversion of points

Part D. Building a first tool for inversion + radical axis


Section 2. Orthogonal Circles through Points

Part E. Orthogonal Circle Given Two Points + One Circle

Part F. Orthogonal Circle Given One Point + Two Circles


Section 3: Tracing Orthogonal Circles and the Radical Axis

Part G. Tracing the Circles Orthogonal to Two Given Circles

Next, carry out Construction -- Tracing Circles Orthogonal to Two Circles but using these CHANGED INSTRUCTIONS for VERSION 4.

Experiment 1. Trace the centers to see the Radical Axis

Experiment 2. Trace the circle d to see a "pencil" of circles

Things to Think About

Part H. Tool for the Radical Axis of Two Circles

Continue with the figure above with circles c1 and c2, the point A on c1 and the circle d through A with center P. (Hide or get rid or traces and loci.)

Experiment