- “Ron is constructing a board with moveable gears for his little brother to play with. He constructs the first
circle gear and puts the second gear right next to the first one. He wants to figure out the distance between the
centers of the two gears so that he can use the correct size band to tie the two together. Use the diagram to
help Ron figure out the distance ofAB.” - Figure 09.03.01
- Students need to include a diagram and a written explanation of their solution.
- Here is the solution:
- Figure 09.03.02
- The distance is approximately 14.4.
III.MeetingObjectives
- Students will solve problems involving common external tangents of circles.
- Students will solve problems involving externally tangent circles.
IV.NotesonAssessment
- Collect both diagrams and written work from students.
- Does the written work match the diagram?
- Is the diagram clear?
- Is the written explanation clear?
- Did the students arrive at the correct answer?
- Provide students with correction/feedback.
Arc Measures
I.SectionObjectives
- Measure central angles and arcs of circles.
- Find relationships between adjacent arcs.
- Find relationships between arcs and chords.
II.ProblemSolvingActivity-ThePieDilemma
- Here is the problem.
- “Jessica has made a delicious blueberry pie. Unfortunately, she cut the pie into uneven pieces.”
- Figure 09.04.01
- “Given the diagram, help Jessica figure out the dimensions of each section of the pie based on her uneven
cuts.” - Find the measure of arcCD, arcACand arcBDCA.
- Students need to use a diagram, a written explanation and a worksheet showing all work.
- Solution:
- The angle of arcABis 80◦.
- SinceABandCDare congruent, thenCDis also 80◦.
- ArcAC= 180 − 80 = 100 ◦
- ArcBDCA= 100 + 180 = 280 ◦
III.MeetingObjectives
- Students will find the measure central angles and arcs of circles.
Chapter 5. Geometry TE - Problem Solving