9.8: Chapter 9 Review
Difficulty Level: At Grade
Created by: CK-12
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 9-2
- 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*}.
- Minor Arc
- An arc that is less than \begin{align*}180^\circ\end{align*}.
- Major Arc
- An arc that is greater than \begin{align*}180^\circ\end{align*}. 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 9-3
- In the same circle or congruent circles, minor arcs are congruent if and only if their corresponding chords are congruent.
- Theorem 9-4
- The perpendicular bisector of a chord is also a diameter.
- Theorem 9-5
- If a diameter is perpendicular to a chord, then the diameter bisects the chord and its corresponding arc.
- Theorem 9-6
- 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 9-8
- Inscribed angles that intercept the same arc are congruent.
- Theorem 9-9
- An angle that intercepts a semicircle is a right angle.
- Inscribed Polygon
- A polygon where every vertex is on a circle.
- Theorem 9-10
- A quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
- Theorem 9-11
- 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 9-12
- 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 9-13
- 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 9-14
- The product of the segments of one chord is equal to the product of segments of the second chord.
- Theorem 9-15
- 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*}.
- Theorem 9-16
- 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*}.
- Standard Equation of a Circle
- The standard equation of a circle with center \begin{align*}(h, k)\end{align*} and radius \begin{align*}r\end{align*} is \begin{align*}r^2=(x-h)^2+(y-k)^2\end{align*}.
Vocabulary
Match the description with the correct label.
- minor arc - A. \begin{align*}\overline{CD}\end{align*}
- chord - B. \begin{align*}\overline{AD}\end{align*}
- tangent line - C. \begin{align*}\overleftrightarrow{CB}\end{align*}
- central angle - D. \begin{align*}\overleftrightarrow{EF}\end{align*}
- secant - E. \begin{align*}A\end{align*}
- radius - F. \begin{align*}D\end{align*}
- inscribed angle - G. \begin{align*}\angle BAD\end{align*}
- center - H. \begin{align*}\angle BCD\end{align*}
- major arc - I. \begin{align*}\widehat{BD}\end{align*}
- point of tangency - J. \begin{align*}\widehat{BCD}\end{align*}
Texas Instruments Resources
In the CK-12 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:
Feb 03, 2016
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