1. Unit 3
Circles

2. Parts of a Circle
Circle – set of all points _________ from a given point called the _____ of the circle.
equidistant C
center
Symbol: C

3. CHORD: a segment whose ________ are on the circle
endpoints

4. RADIUS: distance from the _____ to a point on the circle
center P

5. DIAMETER: distance ______ the circle through its ______
across P
center
Also known as the longest chord.

6. What is the relationship between the diameter and the radius of a circle?OR
D =
½ D
2 r

7. Use P to determine whether each statement is true or false.Q R T S

8. SECANT sounds like second
Secant Line
A secant line intersects the circle at exactly TWO points.
SECANT sounds like second

9. TANGENT: a LINE that intersects the circle exactly ONE time

10. Point of Tangency

11. Secant Radius Diameter Chord Tangent
Name the term that best describes the line.
Secant
Radius
Diameter
Chord
Tangent

12. Central Angles

13. Central Angle : An Angle whose vertex is at the center of the circle
Major Arc
Minor Arc
More than 180°
Less than 180°
ACB P AB
To name: use 3 letters C
To name: use 2 letters B
APB is a Central Angle

14. Semicircle: An Arc that equals 180°
To name: use 3 letters E D
EDF P F

15. THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs are Supplementary

16. measure of an arc = measure of central angle
96˚ D
m AC =
96° B E
m ACB =
276°
m AB =
84°

17. Arc Addition PostulateB
m ABC =
+ m BC
m AB

18. 240 260 m DAB = m BCA = Tell me the measure of the following arcs. D
140
260
m BCA = R
40
100
80 C B

19. CONGRUENT ARCS
Congruent Arcs have the same measure and MUST come from the same circle or congruent circles. C B D 45 45
110 A

20. Distance around the circle
Circumference
Distance around the circle

21. Circumference
2 p r = C or dp = C

22. Find the circumference

23. Arc Length A B

24. Arc Length Example A
5cm
50º B
4.36 cm

25. SECTOR: region bounded by two radii of the circle and their intercepted arcQ O
Area of a Sector

26. Example
6cm
60°

27. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle
INTERCEPTED ARC
INSCRIBED ANGLE

28. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1.
YES; CL C L O T

29. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
NO; QVR 2. Q V K R S

30. To find the measure of an inscribed angle…
160
80

31. What do we call this type of angle? What is the value of x?
How do we solve for y?
The measure of the inscribed angle is HALF the measure of the inscribed arc!!
120 x y

32. 40  112  Examples 3. If m JK = 80, find m <JMK.
4. If m <MKS = 56, find m MS.
112  M Q K S J

33. If two inscribed angles intercept the same arc, then they are congruent.
72

34. 5x = 2x +9 x = 3 In J, m<3 = 5x and m< 4 = 2x + 9. Example 5
Find the value of x. 3 Q D J T U 4
5x = 2x +9
x = 3

35. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

36. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

37. y = 70 z = 95 110 + y =180 z + 85 = 180 Example 8 Find y and z. z 110

38. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
180
diameter

39. Example 6
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
4x – 14 = 90 H K
x = 26 N G

40. Example 7
In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x.
6x – 5 + 3x – 4 = 90 H 2 K
x = 11 1 N G