josh+hoffmans+chapter+9+wiki

=9.1 Chords and Arcs=

__**Semicircle**__- The degree measure is always 180°.
= = =9.2 Tangents to Circles=

Definitions:
__Secants__- A secant to a circle is a line that intersects the circle at two points.

__Tangent-__ A tangent is a line in the plane of the circle that intersects the circle at exactly one point. |tangent __Tangent Theorem__- A line is perpendicular to a circle's radius that is drawn to the point of tangency if the line is tangent.

Radius and Chord Theorem- The radius of a circle bisects the chord that it is perpendicular to. =9.3 Inscribed Angles and Arcs=

Definitions:

__Inscribed Angle__-An angle who has sides that are the chords of a circle and whose vertex lies on the circle. [|inscribed angle] __Inscribed Angle Theorem__-An inscribed angle's measure is half the measure of the intercepted arc.

__Right-Angle Corollary__-An inscribed angle is a right angle if it intercepts a semicircle

__Arc-Intercept Corollary__-Two inscribed angles have the same measure if they intercept the same arc.

=9.4 Angles Formed by Secants and Tangents=

Classification of Angles with Circle: There are three cases and theorems to consider, according to the placement of the vertex of the angles. Case 1: Vertex is on the circle Theorem 1- If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle formed is __½__ the measure if its intercepted arc. |vertex inside circle Case 2: Vertex is inside the circle Theorem 2- the measure of an angle formed by two secants or chords that intersect in the interior of a circle is __½__ the __sum__ of the measures of the arcs intercepted by the angle and its vertical angle.

Case 3: Vertex is outside the circle Theorem- The measure of angle formed by two secants that intersect in the exterior of a circle is __½__ the __difference__ of the measure of the intercepted arcs.

=9.5 Segments of Tangents, Secants, and Chords=

Theorem: __Segment formed by tangents:__ If two segments are tangent to a circle from same external point, then the segments __are congruent.__ __Segments formed by secants:__ Part 1- If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals __the other__ Whole x Outside = Whole x Outside

Part 2- If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and external segment equals Whole x Outside = Tangent Squared

__Segments Formed by Intersecting Chords-__ If two chords intersect a circle, then the product of the lengths of the segments of one chord equals the __product of lengths of the regular of the other chord.__

=9.6 Circles in the Coordinate Plane=

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