G E O M E T R Y

Radius (or Radii for plural)
A
• The segment joining the center of a circle to a point on the circle.
O

A
Chord
C o
B
• A segment joining two points on a circle
• Example: AB
• Example: OA

A
C
Chord
B
• A segment joining two points on a circle
• Example: AB

Diameter
• A chord that passes through the center of a circle.
• A diameter = 2 radii.
• Example: AB
A
O
B

Circumference
• Distance around the edge of a circle. This is a unit measurement not a degree measurement.
• πD or 2πr where D = diameter and r = radius
• Section of the edge of a circle or length of the arc in units =
Total Circumference x intercepted arc or angle degree
360

Secant
• A line that intersects the circle at exactly two points.
• Example: AB
A
C
O
D
B
D
B
O
A
C

A
C
B
Tangent
• A line that intersects a circle at exactly one point.
• Example: AB

Arc
• A figure consisting of two points on a circle and all the points on the circle needed to connect them by a single path.
A
• Example: arc AB
B

B
Intercepted Arc
A
• An arc that lies in the interior of an angle .
C
• Example: arc AC

Central Angle
• An angle whose vertex is at the center of a circle.
• Central angle = intercepted arc
• Example: Angle ABC
B
A
C

B
Inscribed Angle
A
C
• An angle whose vertex is on a circle and whose sides are determined by two chords.
• Inscribed angle =
½ intercepted arc
• Example: Angle ABC

Chord Theorems
• Chords equidistant from center point are equal
• Segment from the midpoint of a chord to the center of the circle is perpendicular
• Chords are congruent if the corresponding arcs are congruent.

Inscribed Angle Theorems
• Point on the arc of a semicircle will connect to each end of the diameter to make a right triangle.
• Inscribed Angles of congruent arcs are congruent
• Inscribed angles of the same arc are congruent.

Two Secants intersecting inside the circle
D
F
B
C
A
• Two intercepted arcs: arc AC and arc DF
• Segments values:
AB ·BF = CB·BD
• Angle Values: Add two intercepted arcs and divide by 2 to get angle FBD

A
Secant and Tangent intersecting outside the circle
A
D
B B
• Angle measure: (arc
AD – arc AC)  2 =
 B
E
C • Segment measure:
AB ²=BD·BC
C D

Secant and Tangent on the circle
A
B
C
• Angle measure: same as inscribed angle,  ABD
= arc BD  2
• No pattern for the segment measures
A
D

Two secants intersecting outside the circle
• Segment measures:
AD ·AE = AB·AC
D
B
E
C
• Angle measure:
(arc DB – arc EC) 
2 =  EAC
A

D
Two Tangent lines
C
• Segment measures:
AB = AD
B
• Angle Measure: (arc
BCD – arc BD)  2 =
 BAD
A

Equation of a Circle
• (x-h) ²+(y-k)²=r²
• (h,k) = center and r = radius
• Simplify equations
• Graph using the center point first then plot the radius