Pema303

Objectives:**
 * Chapter 9**
 * 9.1
 * Define a circle and its assoceated 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.

__**Definitions**__ __Circle__- A circle is the set of all point in a plan thatare eguidistant in a plan in a plan known as the center of the circle. __Radius__- is a segment form center of the circle to a point on the circle. __Chord__- is a segment where endpoints line on a circle. __Diameter__- is a arc that contains the center ofa circle. __Arc__- is a unbroken part of a circle. __Endpoints-__ the points are called the "endpoints" of the arc. __Semi-circle__- is an arc-with endpoints, are endpoints of a diameter. __Minor arc__- of a circle an arc that shorter than a semicircle of that circle. __Major arc__-of a circle an arc that is longer that a semicircle of that cirlce. __Central angle__- of a cicle is a angle in the plane of a circlewhoes vertex is the enter of the circle. __Entercepted arc__-whoes endpoints lie on the side dan arc angle and whose onther points lie in the interior of the angle is the "intercept arc" __Degree measure of arcs__- the degree measured of a minor arc is the measured of its entral angle.. __Arc length__- if r is the radius of a circle and M is a degree measure of an arc of the circle, then the length, L, of the arc is given by the following __Chord and Arc theorem__-In a circle, or in congruent circle, arcs of congruentchords are half. Objectives** Understand the geometry of a radius perpendicular to a chord of a circle.
 * 9.2
 * Define tangents and secants of circles.
 * Understand the relationship between tagents and certain radii of circles.

__Secant__- circle is a line the intersects the circle at two points. __Tangent__- Is a line in the plane of a circle that intersects the circleat exactly one point, which is known as the point of tangency. __Point of Tangency__- A line in a plane that intersects the circle of axactly on point. __Tangent Theorem__- If a line is tangent to a circle then the line in half.
 * __Definitions__**

Objectives** Debelop adn use the inscrbed angle Theorem and its corollaries. __Inscribed angle__- An angle whose vertex lies on a circle and whose sides are chords of the circle. __Inscribed Angle Theorem__- The measure of an angle inscribed 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 right angle. __Arc-Intercept Corollary-__ If an inscribed angle intercepts a semicircle, then the angle is a right angle. __Arc- Intercept Corollary__- If two inscribed angle intercept the same arc, then they have the same measure. Objectives** > __**Theorems**__ > **Theorem Pg.589** > If the tangent and a cecant/ or chord intersects on a circlle at eh point of tangency, then the measre of the angle formed is half the measure of the intercepted arc. > **Theorem 9.4.2** > The measure of an angle formed by two secants or chords that intersect in the interior of a circle is half the sum of the neasures of the arc intercepted by the angle and its vertical angle. > **Theorem 9.4.3** > The measure of an angle formed by two secants that intersect in the exterior of a circle is half the difference of the measure off the intercept. > **9.5 > __Objectives__**
 * 9.3
 * Define inscrbed anle adn itercepted arc.
 * __Definitions__**
 * 9.4
 * Define angles formed by secants and tangents of circles.
 * Develop and use theorems about measures of arcs intersepted by theese angles.
 * 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.
 * __Theorems__**
 * Theorem 9.5.1**- If two segments are tangent to a circle fro the same external point, the segments are congruent.
 * Theorem 9.5.2**- If two secants intersect outside a circle, the product of the lengths of one seccant segment and its external segment equals the other.
 * Theorem 9.5.3**- If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segments equals Tangent squared.
 * Theorem 9.5.4-** If two chords intersect inside a circle, then the prodct of the lengths of the segments of one chord equals the product of length to the reg. of the other chord.


 * 9.6**
 * __Objectives__**
 * Develop and use the equation of a circle.
 * Adjust the equation for a circle to move the center in a coordinate plane.