Lesson 9-9: Circle Applications

Geometry Circles

Lesson 9-9: Circle applications

Objectives:

 Students will apply the related theorems to solve a variety of proofs  Students will apply theorems to multistep circle problems

Procedure:  HW discussion  Do Now! Review  5 Practice Stations

Homework: Castle learning Circle practice test 9-9 and study sheet Name:______

Mixed Applications: Draw diagrams as needed!!!

2. Which is an equation of the locus of points that are 3 units from the point (3, 2)?

1. (x − 3)2 + (y − 2)2 = 9 2. (x − 3)2 + (y − 2)2 = 3 3. (y − 2) = (x − 3) + 3 4. y = 3x − 7

3. Cerise waters her lawn with a sprinkler that sprays water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an angle of 300°, as shown by the shaded area in the accompanying diagram. What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?

4. From the diagram below, find the length . DE = 15m Round your answer to the nearest hundredth.

Try these! Think about it!!!! The angle of a sector in a given circle is 40 degrees and the area of the sector is equal to 20 cm 2. Calculate the arc length of the sector. Name:______Geometry Lesson 9-9 Circles

Station #1: Angles Station #1 Cut out and match all the answers!

85 100 63

37 30 80

50 60 25 Name:______Geometry Lesson 9-9 Circles

Station #2: Segments

AC is the diameter Radius =9 CB=24; AB=30

Is BC a tangent?

4) In the diagram below, is a tangent to circle O at point S, is a secant, , , and . What is the value of x? Name:______Geometry Lesson 9-9 Circles

Station #3: Proofs

1) Proof warm up question:

In the accompanying diagram of circle O, diameter is drawn, tangent is drawn to the circle at B, E is a point on the circle, and . Which of the following statements is true?

1. ΔABE is congruent to ΔCAB. 2. ΔABE is similar to ΔCAB. 3. ΔABE is not similar to ΔCAB.

2) Given: In circle O, Diameters LM,NP Prove: LN@ MP

1)In circle O, Diameters LM,NP 1) Given

2) LON  POM 2)

3) 3) All radii are congruent.

4) LON  POM 4)

5) 5) CPCTC

6) LN@ MP 6)

Name:______Geometry Lesson 9-9 Circles

Station #4: arc length and sectors

1) Find the circumference of a circle in which an arc contains 60o and has a length of 3 pi.

3) Circle O represents a pattern for Pam’s hip-hop skirt. Find the area of the sector MON that she must cut out to the nearest hundredth. This is the only material she has left to finish a fancy embellished pocket. The pattern says she needs 16 sq. cm. Will Pam be able to embellish her skirt? Explain. Name:______Geometry Lesson 9-9 Circles

Station #5: Inscribed quads and polygons

Find each:

mDC mS FAB mS DCG

mS GDC mS DGC

3) Find the measure of each angle of the quadrilateral if AD is a diameter. mA  750 mAB = 300 mBC = 300

Find angles B, C and D.