Tangent Lines
I.SectionObjectives
- Find the relationship between a radius and a tangent to a circle.
- Find the relationship between two tangents draw from the same point.
- Circumscribe a circle.
- Find equations of concentric circles.
II.Cross-curricular-Design
- Have students look at the following image from Wikipedia.
- This is Figure 09.02.01
- http://www.en.wikipedia.org/wiki/File:Concentric_(PSF).png
- This is a picture of concentric circles.
- Have students discuss the characteristics of concentric circles.
- Are they similar?
- How can we design a concentric circle?
- Ask the students to create a black and white art design using concentric circles.
- Students will need white paper, black pencil or marker, a compass.
- Have the students work to create their own design.
- Also have them insert one tangent line somewhere in the design.
- Allow time for students to share their work when finished.
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III.TechnologyIntegration
- This is a very fascinating website for students to explore.
- http://www.cut-the-knot.org/Curriculum/Geometry/TangentTwoCirclesI.shtml
- In working with this website, students will be manipulating the center of one of the circles.
- They can click on the center and drag the center anywhere that they wish to.
- When they do this, they will alter the diagram of the two circles and their tangents.
- It is a great visual and very interactive.
IV.NotesonAssessment
- Assess student work with the art design.
- Is the design of the concentric circles accurate?
- Are the circles organized around a common center?
- Is there a tangent in the design?
- Does the student understand what a tangent is based on what he/she has drawn?
- Provide students with feedback as needed.
Common Tangents and Tangent Circles
I.SectionObjectives
- Solve problems involving common internal tangents of circles.
- Solve problems involving common external tangents of circles.
Chapter 3. Geometry TE - Enrichment