Download Tangent and Chord Properties

Tangent and Chord Properties
Segments and Lines in relation to
circles
Review of Terms and Ideas
Tangent
Line or segment that touches a circle at one
point ( point of tangency)
This line or segment is perpendicular to the
radius at this point
Tangent Segments
Two segments tangent to a circle from the same
point outside the circle are congruent.
These lines would form an Isosceles Triangle,
Why?
Tangent Circles
Two circles that are tangent to each other, touch
at only 1 point
Internally Tangent – one circle inside the other
Externally Tangent
Example
Example
Central Angle and Minor Arc
Central angle is the same as the arc it forms,
formed by 2 radii at the center
Minor arc is angle formed
on the circle between the
two radii, same as the
central angle
Central Angle
Has vertex at the center of the circle, both sides
are radii of the circle
Chords
Segment insides a circle, connecting two points
on the circle
Diameter is the longest chord in a circle
Inscribed Angles
Vertex of angle is on the circle and sides are
chords of the circle
Chord Central Angle
If two chords in a circle are congruent, then they
determine two central angles that are congruent
Chord Arcs
If two chords in a circle are congruent, then
their intercepted arcs are congruent
Chord Distance to Center
Two Congruent chords in a circle are equidistant
to the center of the circle
Perpendicular to a Chord
The radius perpendicular to the chord will bisect
the chord
Perpendicular Bisector of a Chord
The perpendicular bisector of a chord passes
through the center of the circle
Examples
Examples
Terms
Congruent Circles – same radius length
Concentric Circles – same center different radii
Radius – segment from center to any point on circle
Chord – segment connecting any 2 points on circle
Diameter- chord that goes through the center of the circle
Tangent – segment or line that touches the circle at one point
Central Angle – is the angle formed by 2 radii at the center of
the circle
Minor Arc – arc formed between 2 radii, measured in degrees
Major Arc – larger arc formed by 2 radii
Semicircle – half of a circle formed by diameter
HW
Pg 313 1,2 and 5
Pg 320 4,6,11, and 12 Honors 15