10.1: The Circle
Circle- Set of all points in a plane that are equidistant from the center. A line from the center to any point on the circle is a radius.
2+ circles with the same center are cocentric.
Th. If a radius is perpendicular to a chord, it bisects that chord.
Th. If a radius bisects a non-diameter chord, it is perpendicular to it.
Th. The perpendicular Bisector of a chord passes thru the center of the chord
10.2 Congruent Chords
Th. If two chords are equidistant from the center, they are congruent.
Th. If two chords are congruent, they are equidistant.
10.3 Arcs
Minor= arc whose points are on or between the sides of a central angle.
Major- Arc whose points are on or outside of a central angle.
Th. If two central angles of a circle are congruent, than their intercepted arcs are too, and thus the corresponding chords are congruent.
Th. If two chords are congruent, than the corresponding arcs are too and thus so are the central angles.
10.4 Secants/Tangents
Tangent lines are perpendicular to the radius drawn to the point of contact.
If a line is perpendicular to a radius at its outer endpoint, then it is tangent to the circle.
Th. If two tangent lines are drawn from a single point than the lines are congruent.
10.5 Angles of a circle
If the point is inside of the circle it is half the sum of the intercepted arcs. If the point is on the circle, its just half the arc it intercepts. and if its outside the circle, it is half of the difference of the intercepted arcs.
10.6 more arc angle theorems
If two inscribed or tangent chord angles intercept congruent arc, they are congruent.
The sum of a tangent tangent angle and its minor arc is 180.
10.7
If a quad is inscribed in a circle, than opposite angles are supp.
10.8
If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord.
If a tangent segment and a secant segment are drawn from an external point to the circle, then the square of the tangent segment is equal to the measures of the entire secant segment and its external part.
If two secant segments are drawn from an external point to a circle, than the product of the entire secant and its external part of one is equal to the product of the entire secant and its external part of the other.
