Geometry
Chapter 10
Study Guide
I.
Vocabulary
A. Chord: A Segment whose endpoints are on the circumference of the
circle
B. Secant: A line that intersects a circle at two points
C. Tangent: A Line that intersects a circle at exactly one point
D. Central Angle:
1. An angle whose vertex is the center of the circle,
2. The measure of the central angle is the same as its arc
E. Minor Arc: Uses two letters, measures less than 180
F. Major Arc: Uses three letters, measure is greater than 180
G. Inscribed Angle:
1. An angle whose vertex is on the circumference of the circle
2. The measure of an inscribed angle is always half the measure of
the intercepted arc
H. Diameter: Cuts a circle in half, measures exactly 180
II.
Theorems
A. 10.3 (Congruent Chords and Arcs)
Two minor arcs are congruent if and only if their corresponding
chords are congruent
B. 10.4 (Perpendicular Bisectors)
If a chord is a perpendicular bisector of another, then the first chord is
a diameter
C. 10.5 (Converse Perpendicular Bisectors)
If a diameter of a circle is perpendicular to a chord, then the diameter
bisects the chord and its corresponding arc
D. 10.6 (Congruent Chords)
Two chords are congruent if and only if they are equidistant from the
center of a circle
E. 10.9 (Inscribed Right Triangles)
A right triangle can be inscribed if and only if the hypotenuse is the
diameter
F. 10.10 (Inscribed Quadrilaterals)
A Quadrilateral can be inscribed if and only if it’s opposite angles are
supplemental
G. 10.12 (Angles Inside the Circle)
Two Chords intersect insde a circle, then the measure of each angle is
half the sum of the measures of the intercepted arcs (Ex Pg. 861)
H. 10.13 (Angles Outside the Circle)
If two segments (Secants or Tangents) intersect outside a circle, then
the measure of the angle formed is one half the difference of the
measures of the intercepted arcs (Ex Pg. 681)
I. 10.14 (Inside Segments of Chords)
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 lengths of the
segments of the other chord (Ex Pg. 689)
J. 10.15 (Exterior Segments of Chords)
If two secants share the same endpoint outside a circle, then the
product of the length of the whole secant segment and its exterior
segment is equal to the product of the whole second secant and its
exterior segment. (Ex. Pg. 690)
III.
Graphing Circles
A. Standard Form
(x – h)2 + (y – k)2 = r2
B. Center is at (h, k) The opposite of h & k from the formula above.