Chapter 11: Terms
Terms
Definition
Chord
A segment whose endpoints are on a circle.
Secant
A line that intersects a circle in two points.
Tangent
A line in the plane of a circle that intersects
the circle in exactly one point.
Point of
Tangency
The one point where a tangent intersects a
circle.
Tangent
Segment
A segment with one endpoint at the point
of tangency of a circle and the other
endpoint on the tangent line.
Minor Arc
An arc less than 180 degrees.
Major Arc
An arc greater than 180 degrees.
Explanation
Diagram
Measure of a
Minor Arc
The measure of the central angle of the arc.
Measure of a
Major Arc
The difference of 360˚ and the measure of
the related minor arc.
Semicircle
An arc whose central angle measures 180˚.
Congruent
Circles
Two circles that have the same radius.
Congruent
Arcs
Two arcs that have the same measure.
Arc length
A portion of the circumference of a circle.
Inscribed
Angle
An angle whose vertex is on a circle and
whose sides contain chords of the circle.
Intercepted
Arc
An arc that lies in the interior of an
inscribed angle and has endpoints on the
angle.
Inscribed
Polygon
A polygon whose vertices intersect with a
circle. The circle is said to be circumscribed
about the polygon.
Circumscribed A polygon whose segments are tangent to
Polygon
a circle. The circle is said to be inscribed on
the polygon.
Theorems Postulates and Formulas
Name
Theorem 11.1
Theorem 11.2
Theorem 11.3
Arc Addition Postulate
(Postulate 16)
Arc Length
Theorem 11.4
Theorem 11.5
Words
If a line is tangent to a circle
then it is perpendicular to the
radius drawn at the point of
tangency.
In a plane, if a line is
perpendicular to a radius of a
circle at its endpoint on the
circle, then the line is tangent to
the circle.
If two segments from the same
point outside a circle are
tangent to the circle, then they
are congruent.
The measure of an arc formed
by two adjacent arcs is the sum
of the measures of the two arcs.
In a circle, the ratio of the length
of a given arc to the
circumference is equal to the
ratio of the measure of the arc
to 360˚.
If a diameter of a circle is
perpendicular to a chord, then
the diameter bisects the chord
and its arc.
If one chord is a perpendicular
bisector of another chord, then
the first chord is a diameter.
Symbols
Diagram
Theorem 11.6
Theorem 11.7
(Measure of an
Inscribed Angle)
Theorem 11. 8
Theorem 11.9
Theorem 11.10
Theorem 11.11
In the same circle, or in
congruent circles, if two chords
are congruent, then their
corresponding minor arcs and
their corresponding chords are
congruent.
If an angle is inscribed in a circle,
then its measure is half the
measure of its intercepted arc.
If a triangle is inscribed in a
circle is a right triangle, then the
hypotenuse is a diameter of the
circle.
If a quadrilateral can be
inscribed in a circle, then its
opposite angles are
supplementary.
If two chords intersect inside a
circle, then the measure of each
angle formed is one half the sum
of the measures of the arcs
intercepted by the angle and its
vertical angle.
If two chords intersect inside a
circle, then the product of the
lengths of the segments of one
chord is equal to the product of
the lengths of the segments of
the other chord.
x2 + y2 = r2
The equation of a circle with
center at the origin and radius r.
Standard Equation of a In the coordinate plane, the
Circle
standard equation of a circle
with center (h,k) and radius r is
(x – h) 2 + (y – k) 2 = r2