9.8: Chapter 9 Review
Difficulty Level: At Grade
Created by: CK12
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Keywords & Theorems
 Circle
 The set of all points that are the same distance away from a specific point
 Center
 The set of all points that are the same distance away from a specific point, called the center.
 Radius
 The distance from the center to the circle.
 Chord
 A line segment whose endpoints are on a circle.
 Diameter
 A chord that passes through the center of the circle.
 Secant
 A line that intersects a circle in two points.
 Tangent
 A line that intersects a circle in exactly one point.
 Point of Tangency
 The point where the tangent line touches the circle.
 Congruent Circles
 Two circles with the same radius, but different centers.
 Concentric Circles
 When two circles have the same center, but different radii.
 Tangent to a Circle Theorem
 A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
 Theorem 92
 If two tangent segments are drawn from the same external point, then the segments are equal.
 Central Angle
 The angle formed by two radii of the circle with its vertex at the center of the circle.
 Arc
 A section of the circle.
 Semicircle

An arc that measures \begin{align*}180^\circ\end{align*}
180∘ .
 Minor Arc

An arc that is less than \begin{align*}180^\circ\end{align*}
180∘ .
 Major Arc

An arc that is greater than \begin{align*}180^\circ\end{align*}
180∘ . Always use 3 letters to label a major arc.
 Congruent Arcs
 Two arcs are congruent if their central angles are congruent.
 Arc Addition Postulate
 The measure of the arc formed by two adjacent arcs is the sum of the measures of the two
 Theorem 93
 In the same circle or congruent circles, minor arcs are congruent if and only if their corresponding chords are congruent.
 Theorem 94
 The perpendicular bisector of a chord is also a diameter.
 Theorem 95
 If a diameter is perpendicular to a chord, then the diameter bisects the chord and its corresponding arc.
 Theorem 96
 In the same circle or congruent circles, two chords are congruent if and only if they are equidistant from the center.
 Inscribed Angle
 An angle with its vertex is the circle and its sides contain chords.
 Intercepted Arc
 The arc that is on the interior of the inscribed angle and whose endpoints are on the angle.
 Inscribed Angle Theorem
 The measure of an inscribed angle is half the measure of its intercepted arc.
 Theorem 98
 Inscribed angles that intercept the same arc are congruent.
 Theorem 99
 An angle that intercepts a semicircle is a right angle.
 Inscribed Polygon
 A polygon where every vertex is on a circle.
 Theorem 910
 A quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
 Theorem 911
 The measure of an angle formed by a chord and a tangent that intersect on the circle is half the measure of the intercepted arc.
 Theorem 912
 The measure of the angle formed by two chords that intersect inside a circle is the average of the measure of the intercepted arcs.
 Theorem 913
 The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.
 Theorem 914
 The product of the segments of one chord is equal to the product of segments of the second chord.
 Theorem 915

If two secants are drawn from a common point outside a circle and the segments are labeled as above, then \begin{align*}a(a+b)=c(c+d)\end{align*}
a(a+b)=c(c+d) .
 Theorem 916

If a tangent and a secant are drawn from a common point outside the circle (and the segments are labeled like the picture to the left), then \begin{align*}a^2=b(b+c)\end{align*}
a2=b(b+c) .
 Standard Equation of a Circle

The standard equation of a circle with center \begin{align*}(h, k)\end{align*}
(h,k) and radius \begin{align*}r\end{align*}r is \begin{align*}r^2=(xh)^2+(yk)^2\end{align*}r2=(x−h)2+(y−k)2 .
Vocabulary
Match the description with the correct label.
 minor arc  A. \begin{align*}\overline{CD}\end{align*}
CD¯¯¯¯¯¯¯¯  chord  B. \begin{align*}\overline{AD}\end{align*}
AD¯¯¯¯¯¯¯¯  tangent line  C. \begin{align*}\overleftrightarrow{CB}\end{align*}
CB←→  central angle  D. \begin{align*}\overleftrightarrow{EF}\end{align*}
EF←→  secant  E. \begin{align*}A\end{align*}
A  radius  F. \begin{align*}D\end{align*}
D  inscribed angle  G. \begin{align*}\angle BAD\end{align*}
∠BAD  center  H. \begin{align*}\angle BCD\end{align*}
∠BCD  major arc  I. \begin{align*}\widehat{BD}\end{align*}
BDˆ  point of tangency  J. \begin{align*}\widehat{BCD}\end{align*}
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9694.
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Date Created:
Feb 22, 2012
Last Modified:
Aug 15, 2016
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