1. Vocabulary And Properties
Circles
Vocabulary
And
Properties

2. Circle
A set of all points in a plane at a given distance (radius) from a given point (center) in the plane. r 
center

3. Radius
A segment from a point on the circle to the center of the circle. r 

4. Congruent Circles Two circles whose radii have the same measure.
r =3 cm
r =3 cm

5. Concentric Circles
Two or more circles that share the same center. . 

6. Chord A segment whose endpoints lie on the circle.
Segments AB & CD are chords of G  B A G D C

7. Diameter A chord passing through the center of a circle.
Segment IJ is a diameter of G  J G I

8. Secant A line that passes through two points of the circle.
A line that contains a chord.

9. The point of contact is called the
Tangent
A line in the plane of the circle that intersects the circle in exactly one point. ●  ●
The point of contact is called the
Point of Tangency

10. Semicircle is a semicircle
A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. C ●
Three letters are required to name a semicircle: the endpoints and one point it passes through.  B A
is a semicircle

11. Minor Arc An arc of a circle that is smaller than a semicircle.●
Two letters are required to name a minor arc: the endpoints. P  B
PC or CB are minor arcs

12. An arc of a circle that is larger than a semicircle.
Major Arc
An arc of a circle that is larger than a semicircle. C ●  B A
ABC or CAB are major arcs

13. <ABC & <BCD are inscribed angles
An angle whose vertex lies on a circle and whose sides contain chords of a circle. A C B D
<ABC & <BCD are inscribed angles

14. <AKB is a central angle
An angle whose vertex is the center of the circle and sides are radii of the circle. A B  K
<AKB is a central angle

15. m<APB = 2 times m<ACB
Properties of Circles
The measure of a central angle is two times the measure of the inscribed angle that intercepts the same arc. B A 2x P x C
m<APB = 2 times m<ACB
½ m<APB = m<ACB

16. Example If the m<C is 55, then the m<O is 110.
Both angle C and angle O intercept the same arc, AB. B A
110° O
55° C

17. Angles inscribed in the same arc are congruent.
The m<AQB =m<APB both intercept arc AB. A B Q P
m<QAP = m<PBQ
Both angles intercept QP

18. Every angle inscribed in a semicircle is an right angle.

19. Example
Each of the three angles inscribed in the semicircle is a right angle. C D B A E
Angle B, C, and D are all 90
degree angles.

20. Property #4
The opposite angles of a quadrilateral inscribed in a circle are supplementary.

21. Example B 65 A 70 110 C 115 D The measure of angle D + angle B=180
The measure of angle C+angle A=180 B 65 A 70
110 C
115 D

22. Property #5
Parallel lines intercept congruent arcs on a circle.

23. Example
Arc AB is congruent to Arc CD A B D C

24. Formulas
What are the two formulas for finding circumference? C=

25. Answer
C=2 pi r
C=d pi

26. Area of a circle
A=?

27. Answer
A=radius square times pi

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