lattim626

=Chapter 9=

Objectives

 * Define a circle and its associated parts, and use them in constructions
 * Define and use degree measure of arcs.
 * Define and use the length measure of arcs.
 * Prove a theorem about chords and their intercepted arcs.

Definitions

 * Circle-A set of points on a plane equidistant to a given point.
 * Radius- A line segment from the center of the circle to any point on the circle.
 * Chord- A segment with endpoints on the circle.
 * Diameter- A chord that contains the center of the circle.
 * Central Angle- An angle in the plane of a circle whose vertex is the center of the circle.
 * Intercepted Arc- An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle.

Objectives

 * Define tangents and secants if circles.
 * Understand the relationship between tangents and certain radii of circles
 * Understands the geometry of a radius perpendicular to a chord of a circle.

Definitions

 * Secant - A line that intersects the circle at two points.
 * Tangent - A line in the plane of the circle that intersects the circle at exactly one point, which is know as the point of tangency.

Theorems

 * Tangent Theorem - If a line is tangent to a circle, then the line is perpendicular to the radius of the circle drawn to the point of tangency.
 * Radius and Chord Theorem - A radius that is perpendicular to a chord of a circle bisects the chord.
 * Converse of the Tangent Theorem- 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.
 * Theorem - The perpendicular bisector of a chord passes through the center of the circle.

Objectives

 * Define inscribed angle and intercepted arc.
 * Develop and use the Inscribed Angle Theorem and its corollaries.

Definitions

 * Inscribed Angle - An angle whose vertex is on a circle and its sides are chords.

Theorem

 * Inscribed Angle Theorem - The measure of an angle inscibed in a circle is equal to half the measure of the intercepted arc.
 * Right-Angle Corollary - If an inscribed angle intercepts a semicircle, then the angle is a right angle.
 * Arc-Intercept Corollary- If two inscribed angles intercepted the same arc, then they have the same meaure.

Objectives

 * Define angles formed by secants and tangents of circles.
 * Develop and use theorems about measures of arcs intercepted by these angles
 * Definitions - None

Theorems

 * If a tangent and as secant intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc.
 * The measure of an angle formed by two secants of chords that intersect in the interior of a cicle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
 * The measure of an angle is formed by two secants of the intersect in the exterior of a circle is half the difference of the measure of the intercepted arcs.
 * The measure of a tangent-tangent angle with its vertex outside the circle is
 * The measure of a secant-tangent angle with its vertex outside the circle is

Objectives

 * Define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments.
 * Develop and use theorems about the measures of the segments.

Theorems

 * If two segments are tangent to a circle from the same external point, then the segments are congruent
 * If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals
 * If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals
 * If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals

Objectives

 * Develop and use the equation of a circle.
 * Adjust the equation for a circle to move the center in a coordinate plane.