Download Chapter 10 Circle PPT Notes

GEOMETRY
Circle Terminology
Radius (or Radii for plural)
A
O
• The segment joining
the center of a circle to
a point on the circle.
Chord
o
B
A
C
• A segment joining two
points on a circle
• Example: AB
• Example: OA
Chord
B
C
A
• 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
C
• A line that intersects
the circle at exactly
two points.
O
A
C
D
• Example: AB
B
O
D
B
Tangent
B
C
• A line that intersects a
circle at exactly one
point.
A
• 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.
• Example: arc AB
B
A
Intercepted Arc
B
• An arc that lies in the
interior of an angle .
A
• Example: arc AC
C
Central Angle
A
• An angle whose vertex
is at the center of a
circle.
• Central angle =
intercepted arc
• Example: Angle ABC
B
C
Inscribed Angle
B
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
A
B
C
F
• 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
Secant and Tangent intersecting
outside the circle
• Angle measure: (arc
B AD – arc AC)  2 =
B
C • Segment measure:
AB²=BD·BC
B
A
D
E
A
C
D
Secant and Tangent on the circle
A
B
C
A
D
• Angle measure: same as
inscribed angle, ABD
= arc BD 2
• No pattern for the
segment measures
Two secants intersecting outside
the circle
B
D
E
C
A
• Segment measures:
AD·AE = AB·AC
• Angle measure:
(arc DB – arc EC)
2 = EAC
Two Tangent lines
• Segment measures:
AB = AD
C
B
D
A
• Angle Measure: (arc
BCD – arc BD)2 =
BAD
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