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Degree measures of Arcs:

 * Minor Arc=** central angle.
 * Major Arc=** 360 minus the degree measure of the minor arc.
 * Semi Circle=** 180 degrees

Arc Length:
r is the radius, M is the degree measure, and L is the length of the arc. L= M over 360 degrees (2 x pie x r)

r=4 M=30 L=8

30 Divided by 360= .0833 .0833 multiplied by 2=.1666 .1666 multplied by pie=.523 .523 multiplied by 4= 2.092

Chords and Arcs Theorem:
When talking about a circle, or congruent circles, the arcs of the equal chords are the same, or equal.

The Converse Of The Chords and Arcs Theorem:
In congruent circles, the chords of the equal arcs are the same, or equal.

= = =Section 9.2 Tangents to circles:=



That point is **The point of tangency.**
 * Secant:** A line that intersects the circle, crossing it producing two points.
 * Tangent:** A line in a circle that intersects the circle only at one point.

Lets say a line is tangent to a circle, that means that the line is perpendicular to a radius of the circles point of tangency.
 * Tangent Theorem:**

A radius that is perpendicular to the chord, or a chord of the circle bisects the chord.
 * Radius and Chord Theorem:**

A line is perpendicular to a radius, or half point, to the endpoint then the line is tangent to the circle.
 * Converse of the Tangent Theorem:**

The perpendicular bisector of a chord strikes through the exact center of the circle.
 * Theorem:**

=Section 9.3 Inscribed Angles and Arcs:=

the circle, and sides of chords.
 * Inscribed angle:** An angle with a vertex on

equal to 1/2 the measure of the intercepted arc.
 * Inscribed angle Theorem:** An angle in a circle is

Measure of ABC is inscribed in point P and intercepts the arc AC. By the Inscribed Angle Theorem:
 * m of ABC=1/2mAC=1/2[40degrees]=20 degrees**

Then the angle is a right angle, it's proven to be.
 * Right-Angle corollary:** An inscribed angle interferes a semicircle

the same arc, then they are proven to have equal measures.
 * Arc-Intercept corollary:** If two inscribed angles cross through

=Section 9.4 Angles Formed by Secants and Tangents:=

on a circle at the point of tangency. When this happens, the measure of the angle formed is 1/2 the measure of its intercepted arc.
 * Theorem:** A secant [chord] and a tangent cross over

1/2 the sum of the measures of the arcs crossed by the angle and its vertical angle.
 * Theorem:** Two secants form an angle that crosses in the interior of a circle is

is 1/2 the difference of measures of the crossed arcs.
 * Theorem:** Two secants form an angle, that intersect in the exterior of a circle

the circle is 1/2 the difference of the intercepted arc measures.
 * Theorem:** A secant-tangent angle forms a measure with its vertex outside

1/2 the difference of the measures of the intercepts arcs or the measure of the major arc minus 180º.
 * Theorem:** A tangent-tangent angle whose vertex is outside the circle is

=Section 9.5 Segments of Tangents, secants, and chords:=

point, then the segments are the same in lengths.
 * Theorem:** Two segments are tangent compared to a circle from the same outside

of one secant segment and its outside segment equals the product of the secants other lengths and the outside secants.
 * Theorem:** Two secants cross over outside of the circle, and the product of lengths

sum of the lengths of the secant segment and its outside segment equals the length of the tangent segment squared, multiplied by itself.
 * Theorem:** A secant and a tangent cross over outside a circle, then the

lengths of the segments other chord.
 * Theorem:** Two chords cross eachother in the internal of the circle, then the sum of the

=Section 9.6 Circles in the Coordinate Plane:=

http://www.cut-the-knot.org/Curriculum/Geometry/AnglesInCircle.shtml__