- 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.ProblemSolvingActivity-LawnSprinklers
- Here is the problem.
- “Tomas is putting in a sprinkler system in his back yard. He has divided the yard into six square sections.
Inside the center of each square he has planted a sprinkler. The sprinkler spray extends to a distance of 56 feet.
If this is the case, how much area will Tomas cover with his six sprinklers? Here is a diagram of one of the
square plots to help you out.” - Figure 09.02.01
- Tell students to show all of their work in their answer.
- Solution:
- 56 is the radius, so 112 is the diameter of the circle of the spray.
- This is also the side length of one of the square.
- Since we are looking for area, the formula for area of a square iss^2
- A= 1122 = 12 ,544 feet.
- For six squares we multiply this numberx 6 = 75 ,264 feet.
III.MeetingObjectives
- Students will use circles in problem solving.
- Students will use what they have learned about inscribed circles in problem solving.
IV.NotesonAssessment
- Look at all student work.
- Is the work accurate?
- Did the students solve for area and not for perimeter?
- Did the students figure the distance for the diameter?
- Did the students arrive at the correct answer?
- Provide students with feedback/correction.
Common Tangents and Tangent Circles
I.SectionObjectives
- Solve problems involving common internal tangents of circles.
- Solve problems involving common external tangents of circles.
- Solve problems involving externally tangent circles.
- Solve problems involving internally tangent circles.
- Common tangent
II.ProblemSolvingActivity-TheGearProblem
- Here is the problem.
5.9. Circles