stomatt27

=9.1= =Chords and Arcs=

intercepted arc- Is an arc whose end points lie on the sides of the angle and other points lie on the interior.
__**Degree of measure of arcs**__- measure of a minor arc is the meausre of its central angle. measure of a major arc is 360° minus the degree measure of its minor arc. __**Arc length**__ - if r is the radius of a cirlce and m is the degree measure of an arc of the circle, the the lenght, L, of the arc is given by this equasion L = m/360°(2 3.14 r). __**Chords and Arcs Theorem**__ - in a cicrle, or in congruent cirlces, the arcs of congruent chord are similar. the converse of the chords and arcs theorem - in acircle or in congruent circles, the chords of congruent arcs are similar. =9.2=

Tangents to cirlces
__**secant**__ - is a line that has 2 points of intersection in a circle, __**tangent**__ - is a line in a plane of the circle that intersects the circle at exacly one point. __**point of tangency**__ - is a line in a plane of the circle that intersectsthe circle at exacly one point __**Tangent theorem**__ - if a line is tangent to a circle, then the line is perpendicular to radius of the circle drawn to the point of tangency. __**Radius and Chord Theorem**__ - A radius that is perpendicular to a chord of a circle bisects a chord. __**Converse of the Tangent theorem**__ - If aline is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle. __**Theorem**__ - the perpendicular bisector of a chord passes through the center of the circle. =9.3= =Inscribed angles and arcs=

__**Inscribed angle theorem**__ - the measure of an angle inscribed in a circle is equal to one- half the measure of the intercepted arc. __**Right Angle Corollary**__ - If an inscribed angle intersects 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 Tangents= Case 1 - Vertex is on the circle Case 2 - Vertex is inside the circle Case 3 - Vertex is outside the circle. __**Theorem**__ - if a tangent and secant ( or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is one- half the 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 one - half the sum of the measures of the arcs intercepted by the angle and its vertical angle. __**Theorem**__ - The measure of an angle formed by two secants that intersects in the exterior of a circle is one -half the diffrence of the measures of the intercepted arcs. __**Theorem**__ - The measure of a secant- tangent angle with its vertex outside the circle is one-half the diffrence of the measures of the intercepted arcs. =9.5= =Segments of tangents, secants and chords= __**Theorem**__ - If two segments are tangent to a circle from the same external point, then the segments are of equal lenght. __**Theorem**__ - If two segments intersect outside the circle, then the product of the lenghts of one secant segment and its external segment equals the product of the lenghts of the other secant segment and its external segment. (Whole x Outside = Whole x Outside) __**Theorem**__ - If a secant and a tangent intersects outside a circle, then the product of the lenghts of the secant segment and its external segment equals the lenght of a tangent segment squared. Whole x Outside = Tangent² =9.6= =Cicles in the Cordinate Planes= An equation of a circle with the center at (0,0) is : x² + y² = r² An equation of a circle not on (0,0) is : (x-h)²+(y-k)²=r² __Example questions [|Geometry games]__
 * __Theorem__** - The measure of a tangent - tangent angle with its vertex outside the circle is one-half the diffrence of the measures of the intercepted arcs, or the measure of the major arc minus 180
 * __Theorem__** - If two chords intersect inside a circle, then the product of the lenghts of the segment of one chord equals the product of the lenghts of the segments of the other chord. part1 x part2 = part1 x part2.