The most vivid concept in High school Math! Working towards build positive stigma to learners on Geometry concept.

1. 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
A
B
D
C
 G

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

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

9. 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
A semicircle is an arc of a circle whose endpoints
are the endpoints of the diameter.
is a semicircle

C
BA
●
ACB
Three letters are
required to name a
semicircle: the
endpoints and one
point it passes through.

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

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

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

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

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

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.
O
A
B
C
55°
110°

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

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

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

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

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

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

26. Area of a circle
A=?

27. Answer
A=radius square times pi

28. The End
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