The inner circles will be tangent to each other and the original circle. Instructor Suggestions 1. Quickly review how to construct a 120 degree angle and the incenter. There are many short cuts once the first inner circle has been constructed. You may want to mention this and let students come up with another construction method.
Students can work in pairs or independently.
Once the students see that a circle needs to be divided into the same number of central angles as there are inner tangent circles, the discussion can then focus on how to construct various angle measures. You may want to switch gears here and show the students how to use the rotate option in the Transform menu to mark off the angle measures on the circle. After the students have constructed one inner circle they can also use the rotate option to rotate the circle as many times as they want inside the original circle. This method is very fast and the results are pretty neat. Constucting A Circle with Three Inner Tangent Circles Constuction 1.