Circles and Other Related Terms

1. Circles and Other Related Terms
Mathematics 10

2. A circle is the set of all points in a plane that are
at a given distance from a fixed point. The fixed
point P is called the center of the circle and the
given distance is called the radius of the circle.
P
Center
Circles

3. A radius is a line segment from the center to
a point on a circle. (plural form radii)
EX: AC, BC, DC are all radii.
RADIUS
A
B
C
D

4. A diameter is a line segment that connects
two points on the circle and goes through the
center of the circle.
diameter
P
A B
DIAMETER

5. A chord of a circle is a segment whose end points
lie on the circle.
Ex. PR, PS, are chords
Chord

6. A secant line is a line that intersects a circle in
exactly two points.
EX: SF and EF are secants of the circle.
SECANT LINE
S B
E
F
D

7. A tangent line is a line that intersects a circle at
exactly ONE point. The intersection is called
POINT OF TANGENCY.
EX: XD is a tangent line of the circle and point X is
the point of tangency.
TANGENT LINE
D
X

8. An arc is part of a circle connecting two
points of the circle.
- Part of a circle’s edge
EX: 𝑨𝑩, 𝑨𝑿, 𝑿𝑩,
Arc
P
B
Arc
A
X

9. A minor arc is an arc that is less than 180°
- Use two letters to label minor arc. EX: 𝑨𝑩,
A major arc is an arc that is greater than 180°
- Use three letters to label minor arc. EX: 𝑨𝑿𝑩
Minor Arc
B
MINOR and MAJOR Arc
A
P
Major Arc
X

10. A central angle is an angle whose vertex is the
CENTER of the circle.
EX:
An Intercepted arc is an arc that is cut off by the
sides of an angle.
EX: 𝒂𝒓𝒄 𝑨𝑩, is the
intercepted arc
Central Angle and Intercepted Arc

11. The measure of a central angle is equal to
the measure of the intercepted arc.
Central Angle and Intercepted Arc

12. The measure of a central angle is equal to
the measure of the intercepted arc.
Central Angle and Intercepted Arc
Y
Z
O 110
Intercepted Arc
Central Angle

13. Central Angle and Intercepted Arc

14. SUM OF CENTRAL ANGLES
The sum of the measures for the
central angles of a circle is 360º.
360º

15. An inscribed angles is an angle whose vertex on the
circle.
EX: ∠𝑱𝑶𝒀
Inscribed Angle
O
O
J
Y

16. The measure of an inscribed angle is
equal to ½ the measure of the
intercepted arc.
INSCRIBED ANGLE THEOREM

17. The measure of an inscribed angle is
equal to ½ the measure of the
intercepted arc.
INSCRIBED ANGLE THEOREM
Y
55
Inscribed Angle
Intercepted Arc