DaMa117

=9.1 Chords and Arcs=

Objectives- Intercepted Arc- angle whose other points lie in the interior angle Degree Measure of Arcs- Of a minor arc- is the measure of its central angle Of a major arc- is 360 degrees minus the degree measure of its minor arc. Of a semi-circle- 180 degrees
 * Define a circle and its associated parts, and use them in constructions.
 * Define and use the degree measure of arcs.
 * Define and use the length measure of arcs.
 * Prove a theorem about chords and their intercepted arcs.
 * Circle**- Set of all points that are equal distance form the center point
 * Radius**- A segment that goes from the center of the circle to a point in the circle
 * Chord**- A segment with endpoints line on a circle.
 * Diamteter**- A chord that contains nthe center of a circle
 * Central Angle-** of a circle is an angle in the plane of a circle whose vertex is the center of the circle.

Arc Length L=M/360 degrees (2πr)

green-diameter white-radius purple-chord

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9.2 Tangents to Circles
Objectives- each blue line is a tangent Secant- of a circle, is 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, that is called the Point of Tangency.
 * Define tangents and secants of circles.
 * Understand relationships between tangents and certain radii of circles.
 * Understand the geometry of a radius perpendicular to a chord of circle

Theorem-The perpendicular bisector of a chord passes through the center of the circle

9.3 Inscribed Angles and Arcs
Objectives- -Define inscribed angle and intercepted arc. -Develop and use the Inscribed Angle Theorem and its corollaries.



Inscribed Angle-An angle whose vertex lies n a circle and whose sides are chords of the circle.

Right-Angle Corollary-If an inscribed angle intercepts a semicircle, then the angle is a right angle. Arc-Intercept Corollary-If two inscribed angles intercept the same arc, then they have the same measure

9.4 Angles Formed by Secants and Tangents
Objectives- -Define angles formed by secants and tangents of circles. -Develop and use theorems about measures of arcs intercepted by these angles.



9.5 Segments of Tangents, Secants, and Chords
Objectives- -Define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments. -Develop and use theorems about measures of the segments.

9.6 Circles in the Coordinate Plane
Objectives- -Develop and use the equation of a circle. -Adjust the equation for a circle to move the center in a coordinate plane.