Equation of a Circle Notes

where (h, k) is the ______and r is the ______

EXAMPLE:

1. What is the center and radius of the following circle?2. Write the equation for the following circle.

Center = ______

Radius = ______

3. Given a radius of (-2, 12) and a radius of 11 write the equation of the circle.

Central Angle Notes

The measure of a central angle is ______the measure or the intercepted arc created by the angle.

The total number of degrees in a circle is ______.

The total number of degrees in a semicircle is ______.

Together we will answer the following questions.

Use the picture below for the example questions. Tell whether each arc is a major arc, minor arc, or a semi-circle. Then, find the degree measure of each arc.BD is a diameter and CD is an angle bisector.

Ex 1:

Ex 2:

Ex 3:

Ex 4:

Ex 5:

Ex 6:

Ex 7:

Introduction to Circles Worksheet

I. Use the picture at the right to answer the following questions.

  1. Diameter ______
  2. Radius ______
  3. Chord ______
  4. Tangent ______
  5. Minor Arc ______
  6. Major Arc ______
  7. Interior Point ______
  8. Point on the Circle ______
  9. Exterior Point ______
  10. Center Point ______
  11. Central Angle ______
  12. Inscribed Angle ______
  13. Interior Angle ______
  14. Exterior Angle ______

II. Use the picture below for questions 1-10. is a diameter and is an angle bisector. Find the degree measure of each arc and then tell whether each arc is a major arc, minor arc, or a semi-circle.

III. Use the picture below to answer questions 11 -20. and are diameters of the circle.

11.16.

12.17.

13.18.

14.19.

15.20.

III. Find the center and radius from each equation.

21. 22.

23. 24.

IV.

7.8.

9.10.

The relationship between an inscribed angle and its intercepted arc can be written two ways:

Angle measure = ______OR Arc measure = ______

EXAMPLES:

1:=______2: =______

3: =______4: =______

5. =______6. ,

Inscribed Worksheet

I. Identify each picture as showing a central angle, inscribed angle, interior angle, or exterior angle.

1. ______2.______3.______

4. ______5.______6.______

III. Solve for the missing arc measure of angle measure.

7. m<CAD = ______8. <X = ______9. m<V= ______10. m<T = ______

11. , 12. = ______13. x = ______, y = ______

15. x = ______15. = ______16. m<FIG = ______18.z = ______

I. Interior Angle Problems

The formula for interior angles is ______.

Ex 1.Ex 2.

Ex 3. Ex 4.

II. Exterior Angle Problems

The formula for exterior angles is ______.

Ex 5. Ex 6.

Ex 7.Ex 8.

Interior and Exterior Angles Worksheet

1. x = ______2. x = ______3. x = ______

4. x = ______5. x = ______6. x = ______

7. x = ______8. x = ______9. x = ______

10. x = ______11. x = ______12. x = ______

13. x = ______14. z = ______15.

16. x = ______17. y = ______18. x = ______

19. x = ______20. x = ______21. m<J = ______

22. x = ______23. x = ______24. x = ______

22. x = ______23. x = ______

I.Guided Mixed Problems – Central, Inscribed, Interior and Exterior Angles

1. What type of angle?______2.What type of angle?______

is a______.is a______.

=______=______

3. What type of angle?______4.What type of angle?______

is a______.is a______.

=______=______

II. For each circle, solve for the variable.

5. x = ______6. x = ______

7. w = ______8. z = ______

9. p = ______10. t = ______

11. k = ______12. x = ______

13. b = ______14. d = ______

15. s = ______16. y = ______

17. f = ______18. s = ______

19. w = ______20. x = ______


Complex pictures are formed by using multiple types of angles in one picture.

Start with a central angle. Add an inscribed angleAdd an exterior angle

Find = ______Find = _____Find = ____

Find = _____Find = ____

Find = _____Find = ____

Find = ____

Example 1

  1. = ______
  2. = ______
  3. = ______
  4. = ______

Example 2

  1. = ______
  2. = ______
  3. = ______
  4. = ______
  5. = ______
  6. = ______
  7. = ______
  8. = ______

Complex Pictures Worksheet

1. z = ______2. = ______3. x =_____ y = _____

4. x =_____ z=_____5. a =_____ b=_____6. t = ______

w =_____ y=_____

7.8.

9. 10.

Review

. Determining arc length and sector area

1. Find the length of 2. Find the area of the shaded region

II. Use the circle and the following information to answer the questions below.

and are diameters, ,is an angle

bisector of , and

11. Name a minor arc.

12. Name a major arc.

13. Find the measures of all central angles

14. Find the measures of all minor arcs

III. Solve the following problems.

15. 16. x = ______17. x = ______

What type of angle?______What type of angle?______What type of angle?______

18. x = ______19. x = ______20. x = ______

21. x = _____22. x = _____23. x = _____

IV. Find the following values based on Circle A.

24. Find x ______

25. Find ______

26. Find y ______

27. Find z ______

28. Find ______

29. Find ______

30. Find ______

V. Equation of a circle

31. Given what is the center and the radius of the circle?

32. Given a circle centered at (3, 7) with a radius of 12 write the equation.

33. Write the equation for the following circle.

______

Circumference, Area, Arc Length, & Sector Area

Notes Sheet

Use the diagram below to illustrate the following definitions.

circumference –

C = OR C =

area of a circle –

A =

arc length –

Arc Length =

sector area –

Sector Area =

Example: Find the circumference and area of a circle with .C = _____ A = _____

Example: Find the radius of a circle with .r = _____

Example: Find the diameter of a circle with .d = _____

Example: Find the arc length and sector area of the shaded region.

Arc Length = _____ Arc Length = _____ Arc Length = _____

Sector Area = _____ Sector Area = _____ Sector Area = _____

Example: Find the radius of each circle. Round answers to the nearest whole number.

Area of = 40π Arc Length = 80π Area of = 84.8

Shaded Region Shaded Region

r = _____ r = _____ r = _____

Example: Find the central angle measures. Round answers to the nearest whole number.

Arc Length = 1.6π Area of Shaded Region = 1.5πArc Length = 5.5

x = _____ x = _____ x = _____

Exit Ticket

Circumference, Area, Arc Length, & Sector Area

Directions: Calculate the circumference, area, arc length, and sector area of the circle.

Geometry/Trigonometry 2 Fall 2008

Name: ______Date: ______Block: ______

Exit Ticket

Circumference, Area, Arc Length, & Sector Area

Directions: Calculate the circumference, area, arc length, and sector area of the circle.