doka324

9.1

objectives

 * Define a circle and its associated parts, and use the in construction.
 * Define and use the degree measure of arcs.
 * Define sand use he length measure of arcs.
 * Prove a theorem about chords and their intercepted arcs.
 * Circle:** The set of points in a plane hat are equidistant from a given point known as the center of the circle.
 * radius:** A segment that connects the center of a circle with a point on the circle; one-half the diameter of a circle
 * Diameter:** A chord that passes through the center of a circle; twice the length of the radius of the circle
 * Intercepted Arc:** An arc whose endpoints lie on the sides of an inscribed angle
 * Chord:** A segment whose endpoints lie on a circle
 * Arc:** An unbroken part of a circle
 * EndPoint:** A point at an end of a segment or the starting point of a ray
 * Semicircle:** The arc of a circle whose endpoints are the endpoints of a diameter
 * Minor Arc:** An arc of a circle that is shorter than a semicircle of that circle
 * Major Arc:** An arc of a circle that is longer than a semicircle of that circle

Blue Boxes
A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. A **radius**(plural, radii) is a segment from the center of the circle to a point on the circle. A Chord is a segment whose endpoints line on a circle. A **diameter** is a chord that contains the center of a circle.


 * 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 angle and whose other points lie in the interior of the angle is the **intercepted arc** of the central angle.

The degree measure of a minor arc is the measure of its central angle. The degree measure of a major arc is 360 degrees measure of its minor arc. The degree measure of a semicircle is 180 degrees.

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 is given by the following: L=M/360 (2r)

In a circle, or in congruent circles, the arcs of congruent chords are ? In a cirlce or in congruent circles, the chords of congruent arcs are...?

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

Blue Boxes
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**.

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

A radius that is prependicular to a chord of a circle ? the chord.

If a line is perpendicular to a radius of a circle at its endpoint on the circle,then the line is ? to the circle.

The perpendicular bisector of a chord passes through the center of the circle.(therorem)

9.3 Define inscribed angle and intercepted arc. Develop and use the inscribed angle theorem and its corollaries.
 * Objectives**

**Blue Boxes**
The measure of an angle inscribed in a circle is equal to ? the measure of the intercepted arc. If an inscribed angle intercepts a semicircle, then the angle is a right angle. If two inscribed angles intercept the same arc, then they have the same measure example of secant and tangent



9.4

Objectives
Define angles formed by secants and tangents cirlces. Develop and use theorems about measures of arcs intercepted by these angles.

Blue Boxes
If a tangent and a secant( or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is ? the measure of its intercepted arc. The measure of an angle formed by two secants or chords that intersect in the interior of a circle is ? the ? of the measures of the arcs intercepted by the angle and its vertical angle.

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 arcs.

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

The measures of tangent- tangent angle with its vertex outside the circle is ??

9.5

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.

Blue Boxes
If two secants intersect outside a circle, the product of the length of one secant segment and its external segment equals ?. (whole x outside=whole x outside)

If a secant and a tangent intersect outside a circle, then the product of the lengths of the secants segments and its external segment equals whole x outside equals tangent squared

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals ?

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.