pake61

9.1 Chords and Arcs
objective- Define a circle and its associated parts, and use them in constructions. objective- define and use the degree measure of arcs. objective- Define and use the lenghts measure or arcs. objective- prove ea therom about cords and their intercepted arcs.

Definition: Circle
A circle is the set of all points in a plane that are equidistantfrom a given pointin the plane known as the center of the circle. A radius is a segment from the center of the circle to a point of a circle. A chord is a segment whose endspoint on a line on a circle. A diameter is a chord that contains the center of a circle.

If you were not sure what a [|diameter] is this will help. [|word search] The measure all the way across. [|vocab helper] [|Picture]

Definition: Centeral Angle and Intercepted Arc
A central angle of a circle is an angle in the plane of a circle whose vertex is the center of the circle. An arc whose endpoints lie on the side of the angle and whose other points lie in the interior of the angles is the intercepted arc of the centeral angle.

Definition: Degree Measure Of Arcs
The degree measure of a minor arc of its centeral angle. The degree measure of a major arc is 360 degrees minus the degree measure of its minor arc. The degree measure of a semicircle is 180 degrees.

Arc Length
If R is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc given by the following: L=M/360°(2piR)If R is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc given by the following: L=M/360°(2piR)

Here is a visual of a arc.

Chords and Arcs Therom
In a circle, or in congruent circles, the arcs of a congruent chords are congruent.

The converse of the Chords and Arcs Therom
In a circle or in congruent circles, the cords of congruent arcs are.

[|Major Arc]- An arc that is over 180°. The major arc is named by its endpoints.
 * Arc**- an unbroken part of a circle.
 * Endpoints**- Any two distinct points on a circle divide the circle into two arcs.
 * Semi-circle**- an arc whose endpoints of a diameter, called a half circle. Named by endpoints and another point that lies on the arc.
 * Minor arc**- An arc that is less than 180°. THe mainor arc is named by its end points.
 * Central angle**- A central angle of a circle is an angle in the plae of a circle whose vertex is the center of the circle.
 * Intercepted angle**- An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle is the intercepted ard of the central angle.
 * Degree mesure of arcs**- The degree measure of a minor arc is the measure of its central angle. The degree of a major arc is 360° minus the degree measure of its minor arc. The degree measure of a semicircle is 360°.

If you need any more [|definitions] go here!!!!!!!


 * [|Chord]**: Two endpoints that lie on the circles edges.

9.2 Tangent to circles
Objective- Define tangents and secants of circles. Objective- Understand the relationship between tangents and certain radii of circles. Objective- Understand the geometry of a radius perpendicular to a chord of a circle.

Secants and Tangents
a secant to a circle is a line that intersects the circle at two points. A tangent is a line in the plane of the circle that intersects the circle at exactly one point, which is known as the point of tangency.

Tangent theorem
If a line is tangent to a circle, then the line is perpendicular to a radius to a radius of the circle drawn to the point of tangency.

Radius and Chords Theorem
A radius that is perpendicular to a chord of a circle bisects the chords. The spoke is half of the wheel. Half of a circle is a radius. [|wheel]

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

Inscribed Angle Theorem
The measure of an angle inscribee in a circle is equal to half the measure of the intercepted arc.

Right-Angle Corollary
If an incribed 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 Tangent
Objective- Define angles formed by secants and tangents of circles. Objective- Develop and use theorems about measures of arcs intercepted by these angles.

Theorem
If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle is formed is the half measure of its intercepted arc.

Theorem
The measure of an angle formed by two secants or chords that intersect in the interior of a circle is the of teh measures of the arcs intercepted by the angle and its vertical angle.

Theorems of one secant
The measure of an angle formed by two secants that intersect in the exterior of a circle is the of the measures of the intercepted arces.

Theorem
The measure of a secant-tangent angle with its vertex outside the circle is.

Theorem
The measure of a tangent-tangent angle with vertex outside the circle is.

Objective- Define special cases of segents related ot circles Objective- devlop and use theorems about measures of the [|segments]. If two segments are tangent to a circle from the same external point, then the segments are the same.
 * 9.5 Segments of Tangents, Secants and chords**
 * Theorkkskkdksem**

If two secants intersect outside a circle, the product if the lengths of one secant segment and its external segment equals other secant. (WholeXOutside=WholeXOutside)
 * Theorem**

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 the same. (WholeXOutside=Tangent Squared)
 * Theorem**

9.6 Circles in the Coordinate Plane
There are two points woth an x-value of 3: (3,4) and (3,-4).
 * X || Y || Points on graph ||
 * 3 || -or+4 || (3,4) (3,-4) ||
 * -3 || -or+4 || (-3,4) (-3,-4) ||
 * 4 || -or+3 || (4,3) (4,-3) ||
 * -4 || -or+3 || (-4,3) (-4,-3) ||